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Persistence and extinction of nonlocal dispersal evolution equations in moving habitats
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Patrick De Leenheer, Wenxian Shen, Aijun ZhangAbstractThis paper is devoted to the study of persistence and extinction of a species modeled by nonlocal dispersal evolution equations in moving habitats with moving speed c. It is shown that the species becomes extinct if the moving speed c is larger than the so called spreading speed c∗, where c∗ is determined by the maximum linearized growth rate function. If the moving speed c is smaller than c∗, it is shown that the persistence of the species depends on the patch si...
Source: Nonlinear Analysis: Real World Applications - February 9, 2020 Category: Research Source Type: research

Global existence and asymptotic dynamics in a 3D fractional chemotaxis system with singular sensitivity
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Kerui Jiang, Zuhan Liu, Ling ZhouAbstractIn this paper, we investigate the global existence and asymptotic dynamics of solutions to a fractional singular chemotaxis system in three dimensional whole space. We deal with the new difficulties arising from fractional diffusion by using Riesz transform and Kato-Ponce’s commutator estimates appropriately, and establish the local existence of solution. Then with the help of combining the local existence and the a priori estimates, the global existence and uniqueness of solution...
Source: Nonlinear Analysis: Real World Applications - February 8, 2020 Category: Research Source Type: research

Modeling and analysis of recurrent autoimmune disease
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Yancong Xu, Yu Yang, Fanwei Meng, Pei YuAbstractIn this paper, we consider dynamics and bifurcations in two HIV models with cell-to-cell interaction. The difference between the two models lies in the inclusion or omission of the effect of involvement. Particular attention is focused on the effects due to the cell-to-cell transmission and the effect of the involvement. We investigate the local and global stability of equilibria of the two models and give a comparison. We derive the existence condition for Hopf bifurcation a...
Source: Nonlinear Analysis: Real World Applications - February 6, 2020 Category: Research Source Type: research

Multiplicity of clines for systems of indefinite differential equations arising from a multilocus population genetics model
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Guglielmo Feltrin, Paolo GidoniAbstractWe investigate sufficient conditions for the presence of coexistence states for different genotypes in a diploid diallelic population with dominance distributed on a heterogeneous habitat, considering also the interaction between genes at multiple loci. In mathematical terms, this corresponds to the study of the Neumann boundary value problem p1′′+λ1w1(x,p2)f1(p1)=0,in Ω,p2′′+λ2w2(x,p1)f2(p2)=0,in Ω,p1′=p2′=0,on ∂Ω,where the coupling-weights wi are sign-changing ...
Source: Nonlinear Analysis: Real World Applications - February 5, 2020 Category: Research Source Type: research

Stability and cross-diffusion-driven instability in a diffusive predator–prey system with hunting cooperation functional response
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Danxia Song, Chao Li, Yongli SongAbstractThis paper presents a qualitative study of a diffusive predator–prey system with the hunting cooperation functional response. For the system without diffusion, the existence, stability and Hopf bifurcation of the positive equilibrium are explicitly determined. It is shown that the hunting cooperation affects not only the existence of the positive equilibrium but also the stability. For the diffusive system, the stability and cross-diffusion driven Turing instability are investigat...
Source: Nonlinear Analysis: Real World Applications - January 31, 2020 Category: Research Source Type: research

On a class of nonlinear stochastic integral equations
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): R. NegreaAbstractWe prove some existence and uniqueness results for a nonlinear stochastic integral equation using fixed-point theory methods to ensure the convergence of the successive approximations to the unique random solution. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - January 30, 2020 Category: Research Source Type: research

Qualitative analysis on a diffusive age-structured heroin transmission model
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Xi-Chao Duan, Xue-Zhi Li, Maia MartchevaAbstractIn this paper, to understand the impact of spatial heterogeneity of treatment and movement of individuals on the persistence and extinction of heroin spread, we propose a new diffusive heroin transmission model with treatment-dependent age-structure. The basic reproduction number in heterogenous environment R0 of the system is defined, which is consistent with the one deduced from the next generation operator approach R(x). The threshold dynamics in terms of the basic reprodu...
Source: Nonlinear Analysis: Real World Applications - January 28, 2020 Category: Research Source Type: research

Decay rates of solutions to Euler equations with time-dependent damping
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Lina ZhangAbstractIn this paper, we are concerned with the isentropic Euler equations with time-dependent damping like −μ1+tρu for physical parameter μ>0. By using the technical time-weighted energy method, the global existence is proved and the decay estimates are obtained for the solutions of Euler equations. It is interesting that the new decay estimates are dependent on the physical parameter μ. And the decay rates are much better than that obtained by Pan. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - January 28, 2020 Category: Research Source Type: research

Mathematical analysis and optimal control of a cholera epidemic in different human communities with individuals’ migration
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Eric Kokomo, Bongor Danhrée, Yves EmvuduAbstractWe propound a deterministic, nonlinear model for the transmission dynamics of cholera in different human communities with individuals’ migration. The considered different human communities are crossed by a running water which is contaminated by the vibrio cholerae bacterium. The formulated model for each community which is an initial/boundary-value problem constituted of four parabolic partial differential equations, integrates antibiotic treatment, hydration therapy and c...
Source: Nonlinear Analysis: Real World Applications - January 25, 2020 Category: Research Source Type: research

Global solutions to The Vlasov–Poisson–Boltzmann system with weak angular singularity
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Yingzhe Fan, Ping XuAbstractWe prove the global existence of smooth solutions near Maxwellians to the Cauchy problem of non-cutoff Vlasov–Poisson–Boltzmann equation for soft potentials, provided that the weak angular singularity assumption holds and the algebraic decay initial perturbation is sufficiently small. This extends the work of Duan and Liu (2013), in which the case of the strong angular singularity 12≤s<1 is considered, to the case of the weak angular singularity 0<s<12.Our analysis is based on ...
Source: Nonlinear Analysis: Real World Applications - January 25, 2020 Category: Research Source Type: research

Strong solutions to compressible–incompressible two-phase flows with phase transitions
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Keiichi WatanabeAbstractWe consider a free boundary problem of compressible–incompressible two-phase flows with phase transitions in general domains of N-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The compressible fluid and the incompressible fluid are separated by either compact or non-compact sharp moving interface, and the surface tension is taken into account. In our model, the compressible fluid and incompressible fluid are occupied by the Navier–Stokes–Kortew...
Source: Nonlinear Analysis: Real World Applications - January 24, 2020 Category: Research Source Type: research

Existence and uniqueness of solution of free boundary problem with partially degenerate diffusion
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Siyu Liu, Mingxin WangAbstractIn this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - January 22, 2020 Category: Research Source Type: research

Existence of weak solutions to the Keller–Segel chemotaxis system with additional cross-diffusion
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Gurusamy Arumugam, André H. Erhardt, Indurekha Eswaramoorthy, Balachandran KrishnanAbstractIn this paper, we consider the Keller–Segel chemotaxis system with additional cross-diffusion term in the second equation. This system is consisting of a fully nonlinear reaction–diffusion equations with additional cross-diffusion. We establish the existence of weak solutions to the considered system by using Schauder’s fixed point theorem, a priori energy estimates and the compactness results. (Source: Nonlinear Analysis: Rea...
Source: Nonlinear Analysis: Real World Applications - January 21, 2020 Category: Research Source Type: research

Radial stability of periodic orbits of damped Keplerian-like systems
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Zaitao Liang, Fangfang LiaoAbstractIn this paper, by using the third order approximation method, the averaging method and the theory of upper and lower solutions, we study the existence and radial stability of periodic orbits of damped Keplerian-like systems. Two different results are obtained: perturbative and global results. Our results are also applicable to the classical Keplerian-like systems. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - January 21, 2020 Category: Research Source Type: research

A sub-supersolution approach for Neumann boundary value problems with gradient dependence
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Dumitru Motreanu, Angela Sciammetta, Elisabetta TornatoreAbstractExistence and location of solutions to a Neumann problem driven by an nonhomogeneous differential operator and with gradient dependence are established developing a non-variational approach based on an adequate method of sub-supersolution. The abstract theorem is applied to prove the existence of finitely many positive solutions or even infinitely many positive solutions for a class of Neumann problems. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - January 21, 2020 Category: Research Source Type: research