# Nonlinear Analysis: Real World Applications This is an RSS file. You can use it to subscribe to this data in your favourite RSS reader or to display this data on your own website or blog.

**Pulsating type entire solutions originating from three fronts for a bistable reaction–advection–diffusion equation in periodic media**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Guang-Sheng Chen, Shi-Liang WuAbstractThe present paper is to study the pulsating type entire solutions of a reaction–advection–diffusion equation in periodic media with bistable nonlinearity. It is well-known that the equation has three different types of pulsating traveling wavefronts: a bistable front and two families of monostable fronts. The existence of entire solutions originating from two different types of those fronts has also been established by Bu et al. (2016).It is natural to ask whether th...

**Source: **Nonlinear Analysis: Real World Applications - June 14, 2019 **Category: **Research **Source Type: **research

**Global existence and boundedness of classical solutions to a forager–exploiter model with volume-filling effects**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Yuanyuan LiuAbstractThis work is concerned with a chemotactic model for the dynamics of social interactions between two species — foragers u and exploiters v, as well as the dynamics of food resources w consumed by these two species. The foragers search for food directly, while the exploiters head for food by following the foragers. Specifically, the parabolic system in a smoothly bounded convex n-dimensional domain Ω, ut=Δu−∇⋅(S1(u)∇w),x∈Ω,t>0,vt=Δv−&nab...

**Source: **Nonlinear Analysis: Real World Applications - June 14, 2019 **Category: **Research **Source Type: **research

**Large time behavior in a chemotaxis model with logistic growth and indirect signal production**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Wenji Zhang, Pengcheng Niu, Suying LiuAbstractThis paper is concerned with the following chemotaxis-growth system ut=Δu−∇⋅u∇v+μ(u−uα),x∈Ω,t>0,vt=Δv−v+w,x∈Ω,t>0,wt=Δw−w+u,x∈Ω,t>0,in a smooth bounded domain Ω⊂Rn
(n⩾2) with nonnegative initial data and null Neumann boundary condition, where μ>0,α>1. It is stated that if α>n4+12, the solution is globally bounded. Moreover, if μ...

**Source: **Nonlinear Analysis: Real World Applications - June 5, 2019 **Category: **Research **Source Type: **research

**A class of elliptic systems with discontinuous variable exponents and L1 data for image denoising**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Dazhi Zhang, Kehan Shi, Zhichang Guo, Boying WuAbstractThis paper investigates a class of elliptic systems consisting of the p(x)-Laplacian equation and the Poisson equation for image denoising. Under the assumption that p−>max{1,N3}, where p−≔essinfx∈Ωp(x) and N is the dimension of Ω, we prove the existence and uniqueness of weak solutions for the homogeneous Neumann boundary value problem with discontinuous variable exponent p(x) and L1 data. The proof, which is based on Schauder&rsquo...

**Source: **Nonlinear Analysis: Real World Applications - June 4, 2019 **Category: **Research **Source Type: **research

**Coupled systems of Hammerstein-type integral equations with sign-changing kernels**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Robert de Sousa, Feliz MinhósAbstractIn this work we consider a generalized coupled systems of two integral equations of Hammerstein-type where the kernel functions may change sign, as well as remain positive on some subintervals, and the nonlinearities may have discontinuities.Moreover the paper provides other new features:The integral equations contain nonlinearities depending on several derivatives of both variables and, moreover, the derivatives can be of different order on each variable and each equation, whi...

**Source: **Nonlinear Analysis: Real World Applications - June 4, 2019 **Category: **Research **Source Type: **research

**Global dynamics in a reaction–diffusion multi-group SIR epidemic model with nonlinear incidence**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Yantao Luo, Sitian Tang, Zhidong Teng, Long ZhangAbstractIn this paper, a reaction–diffusion multi-group SIR epidemic model with nonlinear incidence in spatially heterogeneous and homogeneous environment is investigated. In general spatially heterogeneous environments, the well-posedness of solutions, including the nonnegativity and ultimate boundedness of solutions, firstly is established. The basic reproduction number R0 is defined. The threshold criteria on the global dynamics of the model are established. That ...

**Source: **Nonlinear Analysis: Real World Applications - June 1, 2019 **Category: **Research **Source Type: **research

**Unfolding homogenization method applied to physiological and phenomenological bidomain models in electrocardiology**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Mostafa Bendahmane, Fatima Mroue, Mazen Saad, Raafat TalhoukAbstractIn this paper, we apply a rigorous homogenization method based on unfolding operators to a microscopic bidomain model representing the electrical activity of the heart at a cellular level. The heart is represented by an arbitrary open bounded connected domain with smooth boundary and the cardiac cells’ (myocytes) domain is viewed as a periodic region. We start by proving the well posedness of the microscopic problem by using Faedo–Galerkin me...

**Source: **Nonlinear Analysis: Real World Applications - June 1, 2019 **Category: **Research **Source Type: **research

**Blow-up analyses in reaction–diffusion equations with Fujita exponents**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Fengjie Li, Hongyan Lin, Bingchen LiuAbstractIn this paper, we study the reaction–diffusion equations with variable coefficients in some bounded domains. At least one of the components of solutions blows up for every initial data in some exponent regions, where the Fujita exponents are determined by the exponents of the sources and the coefficients and the dimension of the domain. We also show the classifications of simultaneous and nonsimultaneous blow-up of the components of solutions. The asymptotic properties a...

**Source: **Nonlinear Analysis: Real World Applications - May 31, 2019 **Category: **Research **Source Type: **research

**Zika virus dynamics partial differential equations model with sexual transmission route**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Kazuo YamazakiAbstractInspired by the system of ordinary differential equations in Agusto et al. (2017) that models Zika virus dynamics by taking into account of both sexual and vector-borne transmissions, we furthermore add diffusive terms in order to capture the movement of human hosts and mosquitoes, considering the unique threat of the sexual transmission route of Zika virus. We conduct complete theoretical analysis. In particular, we show that every initial data that is continuous and non-negative admits a uniq...

**Source: **Nonlinear Analysis: Real World Applications - May 29, 2019 **Category: **Research **Source Type: **research

**Vibrations of a Gao beam subjected to a moving mass**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): B. Dyniewicz, C.I. Bajer, K.L. Kuttler, M. ShillorAbstractThis paper models, analyzes and simulates the vibrations of a nonlinear Gao beam that is subjected to a moving mass or a massless point-force. Such problems arise naturally in transportation systems such as trains or trams. The dynamics of the system as the mass or the force move on the beam are investigated numerically in the cases when the vibrations are about a buckled state, and in the cases when the mass is positive or vanishes. The simulations are compared t...

**Source: **Nonlinear Analysis: Real World Applications - May 29, 2019 **Category: **Research **Source Type: **research

**Wetting fronts in unsaturated porous media: The combined case of hysteresis and dynamic capillary pressure**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): K. Mitra, C.J. van DuijnAbstractThis paper extends the work of van Duijn et al. (2018) where travelling wave solutions for wetting fronts were considered under the presence of only capillary hysteresis effect and only dynamic capillary effect. In this work, we investigate how the gravity driven wetting fronts behave while moving through long vertical homogeneous porous columns, under the combined effect of capillary hysteresis and dynamic capillarity. It is shown that the developed saturation profiles will exhibit n...

**Source: **Nonlinear Analysis: Real World Applications - May 28, 2019 **Category: **Research **Source Type: **research

**Algebraic L2-decay of weak solutions to the magneto-hydrodynamic equations**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Zhaoxia LiuAbstractWe consider the asymptotic behavior of weak solutions to the incompressible magneto-hydrodynamics (MHD) equations in the whole space Rn, n≥2. The algebraic decay of the total energy of weak solutions to Cauchy problem of MHD equations is given by establishing an important inequality on weak solutions of MHD equations. (Source: Nonlinear Analysis: Real World Applications)

**Source: **Nonlinear Analysis: Real World Applications - May 23, 2019 **Category: **Research **Source Type: **research

**Four limit cycles in a predator–prey system of Leslie type with generalized Holling type III functional response**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Yanfei Dai, Yulin Zhao, Bo SangAbstractThis paper, as a complement to the works by Hsu et al [SIAM. J. Appl. Math. 55 (1995)] and Huang et al [J. Differential Equations 257 (2014)], aims to examine the Hopf bifurcation and global dynamics of a predator–prey system of Leslie type with generalized Holling type III functional response for the two cases: (A) system has a unique anti-saddle positive equilibrium, which is not semi-hyperbolic or nilpotent; (B) system has three distinct positive equilibria. For each case, ...

**Source: **Nonlinear Analysis: Real World Applications - May 22, 2019 **Category: **Research **Source Type: **research

**Analysis of a SIR model with pulse vaccination and temporary immunity: Stability, bifurcation and a cylindrical attractor**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Kevin E.M. Church, Xinzhi LiuAbstractA time-delayed SIR model with general nonlinear incidence rate, pulse vaccination and temporary immunity is developed. The basic reproduction number is derived and it is shown that the disease-free periodic solution generically undergoes a transcritical bifurcation to an endemic periodic solution as the vaccination coverage drops below a critical level. Using numerical continuation and a monodromy operator discretization scheme, we track the bifurcating endemic periodic solution as th...

**Source: **Nonlinear Analysis: Real World Applications - May 22, 2019 **Category: **Research **Source Type: **research

**A dynamical model of asymptomatic carrier zika virus with optimal control strategies**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): M.A. Khan, Syed Wasim Shah, Saif Ullah, J.F. Gómez-AguilarAbstractA dynamical model of asymptomatic carrier zika virus model with optimal control strategies is presented. The basic model zika without control and basic mathematical results are obtained. The stability results for the zika model without controls are obtained when the basic reproduction number is less than unity at the disease free case. We show that the zika model without controls is locally and globally asymptotically stable when the basic reproduct...

**Source: **Nonlinear Analysis: Real World Applications - May 16, 2019 **Category: **Research **Source Type: **research

**Threshold dynamics of an age–space structured brucellosis disease model with Neumann boundary condition**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Junyuan Yang, Rui Xu, Jiaxu LiAbstractBrucellosis is a highly contagious zoonosis in the world caused by a group of bacteria from the genus brucella. It can infect both human and animals through eating contaminated food, breathing polluted air, and direct contact of the infected animals. The number of onset cases shows an increase tend in recent years, mainly in pastures and farms. To investigate the dynamics of brucellosis and capture the event of its spread, we propose a novel model that is an attempt for the first tim...

**Source: **Nonlinear Analysis: Real World Applications - May 16, 2019 **Category: **Research **Source Type: **research

**Stability analysis of stationary variational and hemivariational inequalities with applications**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Weimin Han, Yi LiAbstractIn this paper, we provide a comprehensive stability analysis for stationary variational inequalities, hemivariational inequalities, and variational-hemivariational inequalities. With contact mechanics as application background, stability is analyzed for solutions with respect to combined or separate perturbations in constitutive relations, external forces, constraints, and non-smooth contact boundary conditions of the inequality problems. The stability result is first proved for a general variati...

**Source: **Nonlinear Analysis: Real World Applications - May 11, 2019 **Category: **Research **Source Type: **research

**Editorial Board**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): (Source: Nonlinear Analysis: Real World Applications)

**Source: **Nonlinear Analysis: Real World Applications - May 10, 2019 **Category: **Research **Source Type: **research

**Large data analysis for Kolmogorov’s two-equation model of turbulence**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Miroslav Bulíček, Josef MálekAbstractKolmogorov seems to have been the first to recognize that a two-equation model of turbulence might be used as the basis of turbulent flow prediction. Nowadays, a whole hierarchy of phenomenological two-equation models of turbulence is in place. The structure of their governing equations is similar to the Navier–Stokes equations for incompressible fluids, the difference is that the viscosity is not constant but depends on two scalar quantities that measure the effe...

**Source: **Nonlinear Analysis: Real World Applications - May 10, 2019 **Category: **Research **Source Type: **research

**Threshold dynamics of a diffusive nonlocal phytoplankton model with age structure**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Shanshan Chen, Junping ShiAbstractIn this paper, a reaction–diffusion equation with age structure and nonlocal effect for the maturation, growth and spatial distribution of phytoplankton in a water column is derived, and the threshold dynamics for the model is completely classified. It is shown that the death rate and maturation time of the phytoplankton both affect the dynamics of the model. The phytoplankton species could die out if the death rate is greater than a critical death rate. However, when the death rat...

**Source: **Nonlinear Analysis: Real World Applications - May 8, 2019 **Category: **Research **Source Type: **research

**Existence of optical vortices in R2**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Qing Guo, Daomin Cao, Hang LiAbstractOptical vortices are phase singularities nested in electromagnetic waves which constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and Bose–Einstein condensates. The present paper is concerned with the existence of stationary optical vortices wave solutions of nonlinear Schrödinger equations in R2.For the self-focusing case, we consider three types of problems. The fir...

**Source: **Nonlinear Analysis: Real World Applications - May 8, 2019 **Category: **Research **Source Type: **research

**Optimization problems for a viscoelastic frictional contact problem with unilateral constraints**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Mircea Sofonea, Yi-bin Xiao, Maxime CoudercAbstractWe consider a mathematical model which describes the contact between a viscoelastic body and a rigid-deformable foundation with memory effects. We derive a variational formulation of the model which is in the form of a history-dependent variational inequality for the displacement field. Then we prove the existence of a unique weak solution to the problem. We also study the continuous dependence of the solution with respect to the data and prove two convergence results, u...

**Source: **Nonlinear Analysis: Real World Applications - May 8, 2019 **Category: **Research **Source Type: **research

**Radially symmetric growth of necrotic tumors and connection with nonnecrotic tumors**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Junde Wu, Chen WangAbstractIn this paper we study a nonlinear free boundary problem for radially symmetric growth of tumors with necrosis. We show this problem is globally well-posed and find a threshold value σ∗>0, such that if and only if external nutrient supply σ̄≥σ∗, there exists a unique necrotic stationary solution. We prove it is globally asymptotically stable. For σ̄

**Source: **Nonlinear Analysis: Real World Applications - May 5, 2019 **Category: **Research **Source Type: **research

**Global existence of solutions for the Poisson–Nernst–Planck system with steric effects**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Chia-Yu HsiehAbstractIn this work, we study the global existence of a modified Poisson–Nernst–Planck system with steric effects. This model involves cross-diffusion and non-local terms. The main idea of the proof is to approximate the system by truncating the diffusion matrix and apply the Schauder’s fixed-point theorem. Moreover, we obtain L2 uniform in time estimates from the energy inequality (3.5). The global existence then follows. (Source: Nonlinear Analysis: Real World Applications)

**Source: **Nonlinear Analysis: Real World Applications - May 5, 2019 **Category: **Research **Source Type: **research

**A new mathematical model for pricing a mine extraction project**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Michele Pignotti, María Suárez-Taboada, Carlos VázquezAbstractIn this paper, a new mathematical model related to a mining extraction project under uncertainty is proposed. The underlying stochastic factors are the commodity price and the remaining resource, the dynamics of which are introduced. In the stochastic differential equation satisfied by the remaining resource, the extraction rate is involved. The main innovative modelling feature, comes from considering the extraction rate to be proportiona...

**Source: **Nonlinear Analysis: Real World Applications - May 3, 2019 **Category: **Research **Source Type: **research

**On a family of inverse curvature flows for closed convex plane curves**

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Hongxin Guo, Zezhen SunAbstractIn this note we introduce a family of flows for closed convex curves in the plane. Along the flows the enclosed area of the curve is increasing, and the curve remains convex and converges to a circle. The flows include various flows studied by various authors as special cases. (Source: Nonlinear Analysis: Real World Applications)

**Source: **Nonlinear Analysis: Real World Applications - May 1, 2019 **Category: **Research **Source Type: **research

**Convergence rates on periodic homogenization of p-Laplace type equations**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Li Wang, Qiang Xu, Peihao ZhaoAbstractIn this paper, we find some error estimates for periodic homogenization ofp-Laplace type equations under the same structure assumption on homogenized equations. The main idea is that by adjusting the size of the difference quotient of the correctors to make the convergence rate visible. In order to reach our goal, the corresponding flux corrector with some properties are developed. Meanwhile, the shift-argument is in fact applied down to ε scale, which leads to a new weighted ...

**Source: **Nonlinear Analysis: Real World Applications - April 29, 2019 **Category: **Research **Source Type: **research

**An extension of Riesz transform**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Huan Yu, Quansen JiuAbstractIn this paper, we consider the following singular integral Tjf(x)=Kj∗f(x),Kj(x)=xj|x|n+1−β,where x∈Rn,0≤β

**Source: **Nonlinear Analysis: Real World Applications - April 26, 2019 **Category: **Research **Source Type: **research

**Hopf bifurcation of an age-structured prey–predator model with Holling type II functional response incorporating a prey refuge**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Peng YangAbstractIn this paper, an age-structured prey–predator model with Holling type II functional response incorporating a prey refuge is constructed. Through applying the method of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain, we obtain that the model undergoes a Hopf bifurcation at the interior equilibrium which shows that this model has a non-trivial periodic orbit that bifurcates from the interior equilibrium when bifurcation parameter τ crosses the ...

**Source: **Nonlinear Analysis: Real World Applications - April 17, 2019 **Category: **Research **Source Type: **research

**Turing–Hopf bifurcation and multi-stable spatio-temporal patterns in the Lengyel–Epstein system**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Xianyong Chen, Weihua JiangAbstractIn this paper, we consider the Lengyel–Epstein system of the CIMA reaction with homogeneous Neumann condition. Firstly, we derive conditions for existence of Turing/Turing–Hopf bifurcation by analysis of distribution of eigenvalues. Meanwhile, we give the concrete range of diffusion rate c preserving that spatial inhomogeneous Hopf bifurcation occurs based on the existence result in Du and Wang (2010). Secondly, existence of more complex spatio-temporal dynamical behaviors, s...

**Source: **Nonlinear Analysis: Real World Applications - April 17, 2019 **Category: **Research **Source Type: **research

**Patterns and dynamics in the diffusive model of a nutrient–microorganism system in the sediment**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Qian Cao, Jianhua WuAbstractThis paper is devoted to study patterns and dynamics in the diffusive minimal sediment model. Firstly, we analyze nonnegative constant equilibrium solutions and investigate patterns induced by diffusions. Then we study the properties and existence of nonconstant steady states. Moreover, we describe the local bifurcation structure and global bifurcation structure from two positive constant solutions, respectively. The main tools used here include the stability theory, degree theory, bifurcation ...

**Source: **Nonlinear Analysis: Real World Applications - April 14, 2019 **Category: **Research **Source Type: **research

**Vanishing α and viscosity limits of second grade fluid equations for an expanding domain in the plane**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Jitao Liu, Wen-Qing XuAbstractIn this paper, we study the asymptotic behavior of solutions to second grade fluid equations, a model for viscoelastic fluids, in an expanding domain. We prove that, the solutions converge to a solution of the incompressible Euler equations in the whole plane, as the elastic response α and the viscosity ν vanish, and the radius of domain becomes infinite. Meanwhile, we also establish precise convergence rates in terms of ν, α and the radius of the family of spatial domains. ...

**Source: **Nonlinear Analysis: Real World Applications - April 14, 2019 **Category: **Research **Source Type: **research

**Eventual smoothness and stabilization of global weak solutions in parabolic–elliptic chemotaxis systems with logarithmic sensitivity**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Jaewook Ahn, Kyungkeun Kang, Jihoon LeeAbstractA parabolic–elliptic chemotaxis system with non-negative chemotactic sensitivity χ∕v and positive chemical diffusion coefficient η is considered in a smooth bounded domain Ω⊂RN, N≥2 under homogeneous Neumann boundary conditions. We show the existence of at least one global weak solution for χ

**Source: **Nonlinear Analysis: Real World Applications - April 10, 2019 **Category: **Research **Source Type: **research

**The existence and stability of smooth solutions for multidimensional isentropic bipolar hydrodynamic model of semiconductors**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Lingjun LiuAbstractThe present paper is concerned with the existence and stability of smooth stationary solutions to the multidimensional isentropic bipolar hydrodynamic model for semiconductors in a bounded domain Ω∈RN(N=1,2,3) with insulating boundary conditions. The existence of non-constant steady smooth solutions is firstly obtained by the calculus of variations and the maximum principle. It is further shown that the particle densities converge exponentially fast to the steady state solutions. (Source: Non...

**Source: **Nonlinear Analysis: Real World Applications - April 6, 2019 **Category: **Research **Source Type: **research

**Global existence of solutions to a fully parabolic chemotaxis system with singular sensitivity and logistic source**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Mengyao Ding, Wei Wang, Shulin ZhouAbstractIn this paper we study the global existence of solutions to the fully parabolic chemotaxis system: ut=Δu−χ∇⋅(uv∇v)+f(u), vt=Δv−v+u in a smooth bounded domain Ω⊂Rn (n≥3) subject to the non-flux boundary conditions, where χ>0 and the logistic function f∈C1[0,∞) satisfies f(s)≤r−μsγ with r≥0 and γ,μ>0. It is shown that the problem possesses a global and classical solution as ...

**Source: **Nonlinear Analysis: Real World Applications - April 6, 2019 **Category: **Research **Source Type: **research

**The local existence and blowup criterion for strong solutions to the kinetic Cucker–Smale model coupled with the compressible Navier–Stokes equations**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Chunyin JinAbstractIn this paper, we establish the existence and uniqueness of local strong solutions to the kinetic Cucker–Smale model coupled with the isentropic compressible Navier–Stokes equations in the whole space. Moreover, the blowup mechanism for strong solutions to the coupled system is also investigated. (Source: Nonlinear Analysis: Real World Applications)

**Source: **Nonlinear Analysis: Real World Applications - April 3, 2019 **Category: **Research **Source Type: **research

**On weak–strong uniqueness for compressible Navier–Stokes system with general pressure laws**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Nilasis ChaudhuriAbstractThe goal of the present paper is to study the weak–strong uniqueness problem for the compressible Navier–Stokes system with a general barotropic pressure law. Our results include the case of a hard sphere pressure of Van der Waals type with a non-monotone perturbation and a Lipschitz perturbation of a monotone pressure. Although the main tool is the relative energy inequality, the results are conditioned by the presence of viscosity and do not seem extendable to the Euler system. (Sour...

**Source: **Nonlinear Analysis: Real World Applications - April 3, 2019 **Category: **Research **Source Type: **research

**On the existence of global strong solutions to 2D compressible Navier–Stokes–Smoluchowski equations with large initial data**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Bingkang Huang, Lvqiao Liu, Lan ZhangAbstractThis paper studies a fluid–particle interaction model for the evolution of particles dispersed in fluid. This coupled model consists of the Smoluchowski equation for the particle part, and 2D isentropic compressible Navier–Stokes equations for the fluid part. The global existence of strong solutions to the Cauchy problem of the coupled system with large initial data which may contain vacuum is established. (Source: Nonlinear Analysis: Real World Applications)

**Source: **Nonlinear Analysis: Real World Applications - March 31, 2019 **Category: **Research **Source Type: **research

**Traveling waves of a nonlocal dispersal SEIR model with standard incidence**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Shao-Xia Qiao, Fei-Ying Yang, Wan-Tong LiAbstractThis paper is devoted to investigating the traveling wave solutions of a nonlocal dispersal SEIR epidemic model with standard incidence. We find that the existence and nonexistence of traveling wave solutions are determined by the basic reproduction number and the critical wave speed. Through considering a truncate problem, combining with Schauder’s fixed-point theorem and applying a limiting argument, we prove the existence of traveling wave solutions. Meanwhile, the...

**Source: **Nonlinear Analysis: Real World Applications - March 31, 2019 **Category: **Research **Source Type: **research

**Non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Adriana C. Briozzo, María Fernanda NataleAbstractA non-classical one dimensional Stefan problem with thermal coefficients temperature dependent and a Robin type condition at fixed face x=0 for a semi-infinite material is considered. The source function depends on the evolution the heat flux at the fixed face x=0. Existence of a similarity type solution is obtained and the asymptotic behaviour of free boundary with respect to latent heat fusion is studied. The analysis of several particular cases are given. (Source:...

**Source: **Nonlinear Analysis: Real World Applications - March 22, 2019 **Category: **Research **Source Type: **research

**On the number of limit cycles for generic Lotka–Volterra system and Bogdanov–Takens system under perturbations of piecewise smooth polynomials**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Shiyou Sui, Jihua Yang, Liqin ZhaoAbstractIn this paper, we consider the bifurcation of limit cycles for generic L–V system ( ẋ=y+x2−y2±43xy,ẏ=−x+2xy) and B–T system (ẋ=y,ẏ=−x+x2) under perturbations of piecewise smooth polynomials with degree n. After linear transformation, we choose switching line y=0. By using Picard–Fuchs equations, we bound the number of zeros of first order Melnikov function which controls the number of limit cycles bifurcating from the center. It i...

**Source: **Nonlinear Analysis: Real World Applications - March 21, 2019 **Category: **Research **Source Type: **research

**Steady free surface potential flow of an ideal fluid due to a singular sink on the flat bottom**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): A.A. Mestnikova, V.N. StarovoitovAbstractA two-dimensional steady problem of a potential free-surface flow of an ideal incompressible fluid caused by a singular sink is considered. The sink is placed at the horizontal bottom of the fluid layer. With the help of the Levi-Civita technique, the problem is rewritten as an operator equation in a Hilbert space. It is proved that there exists a unique solution of the problem provided that the Froude number is greater than some particular value. The free boundary corresponding to...

**Source: **Nonlinear Analysis: Real World Applications - March 19, 2019 **Category: **Research **Source Type: **research

**Global dynamics of planar quasi-homogeneous differential systems**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Yilei Tang, Xiang ZhangAbstractIn this paper we provide a new method to study global dynamics of planar quasi-homogeneous differential systems. We first prove that all planar quasi-homogeneous polynomial differential systems can be translated into homogeneous differential systems and show that all quintic quasi-homogeneous but non-homogeneous systems can be reduced to four homogeneous ones. Then we present some properties of homogeneous systems, which can be used to discuss the dynamics of quasi-homogeneous systems. Final...

**Source: **Nonlinear Analysis: Real World Applications - March 14, 2019 **Category: **Research **Source Type: **research

**Editorial Board**

Publication date: August 2019Source: Nonlinear Analysis: Real World Applications, Volume 48Author(s): (Source: Nonlinear Analysis: Real World Applications)

**Source: **Nonlinear Analysis: Real World Applications - March 12, 2019 **Category: **Research **Source Type: **research

**Exact boundary controllability and its applications for a coupled system of quasilinear wave equations with dynamical boundary conditions**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Yue Wang, Günter Leugering, Tatsien LiAbstractA constructive method with modular structure is used to obtain the local exact boundary controllability for a coupled system of quasilinear wave equations with local or non-local dynamical boundary conditions. Some applications are given for the chain-like or star-like system of strings coupled via elastic springs, and of strings coupled via Maxwell-type and Kelvin-type viscoelastic springs, respectively. (Source: Nonlinear Analysis: Real World Applications)

**Source: **Nonlinear Analysis: Real World Applications - March 11, 2019 **Category: **Research **Source Type: **research

**Dirichlet problem for a delayed diffusive hematopoiesis model**

Publication date: August 2019Source: Nonlinear Analysis: Real World Applications, Volume 48Author(s): Xuejun Pan, Hongying Shu, Lin Wang, Xiang-Sheng WangAbstractWe study the dynamics of a delayed diffusive hematopoiesis model with two types of Dirichlet boundary conditions. For the model with a zero Dirichlet boundary condition, we establish global stability of the trivial equilibrium under certain conditions, and use the phase plane method to prove the existence and uniqueness of a positive spatially heterogeneous steady state. We further obtain delay-independent as well as delay-dependent conditions for the local stabil...

**Source: **Nonlinear Analysis: Real World Applications - March 4, 2019 **Category: **Research **Source Type: **research

**On a fully parabolic chemotaxis system with nonlinear signal secretion**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Xie LiAbstractThis paper is devoted to the following nonlinear chemotaxis system ut=Δu−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0,τvt=Δv−v+g(u),x∈Ω,t>0,under homogeneous Neumann boundary conditions. Here Ω⊂R3 is a bounded domain with smooth boundary, but not necessarily convex; S(u) satisfies |S(u)|≤|χ|uq with some q>0 and χ∈R; f(u) satisfies f(u)≤a−buα with some constants a≥0, b>0, α≥1; g(u) satisfies g(u)≤...

**Source: **Nonlinear Analysis: Real World Applications - March 4, 2019 **Category: **Research **Source Type: **research

**Optimal control of invasive species through a dynamical systems approach**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Christopher M. Baker, Fasma Diele, Deborah Lacitignola, Carmela Marangi, Angela MartiradonnaAbstractEffectively dealing with invasive species is a pervasive problem in environmental management. The damages that stem from invasive species are well known. However, controlling them cost-effectively is an ongoing challenge, and mathematical modeling and optimization are becoming increasingly popular as a tool to assist management. In this paper we investigate problems where optimal control theory has been implemented. We show...

**Source: **Nonlinear Analysis: Real World Applications - March 4, 2019 **Category: **Research **Source Type: **research

**Monotonicity of the Morse index of radial solutions of the Hénon equation in dimension two**

Publication date: August 2019Source: Nonlinear Analysis: Real World Applications, Volume 48Author(s): Wendel Leite da Silva, Ederson Moreira dos SantosAbstractWe consider the equation −Δu=|x|α|u|p−1u,x∈B,u=0on∂B,where B⊂R2 is the unit ball centered at the origin, α≥0, p>1, and we prove some results on the Morse index of radial solutions. The contribution of this paper is twofold. Firstly, fixed the number of nodal sets n≥1 of the solution uα,n, we prove that the Morse index m(uα,n) is monotone non-decreasing with respect to α. Secondly, we provide a low...

**Source: **Nonlinear Analysis: Real World Applications - February 28, 2019 **Category: **Research **Source Type: **research

**Incompressible limit of non-isentropic compressible magnetohydrodynamic equations with zero magnetic diffusivity in bounded domains**

Publication date: October 2019Source: Nonlinear Analysis: Real World Applications, Volume 49Author(s): Yaobin Ou, Lu YangAbstractThis paper verifies the incompressible limit of the non-isentropic compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in a three-dimensional bounded C4-domain. The uniform estimates in both the Mach number ϵ and the Péclet number κ for the local strong solutions, which exclude the estimate of high-order derivatives of the velocity in the normal directions to the boundary, are established in a short time interval independent of ϵ and κ (κ≤O(ϵβ), 0

**Source: **Nonlinear Analysis: Real World Applications - February 28, 2019 **Category: **Research **Source Type: **research