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Global solutions to 3-D Navier–Stokes–Maxwell system slowly varying in one direction
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Gaocheng YueAbstractThe present paper is devoted to the well-posedness issue of solutions of a full system of the 3-D incompressible magnetohydrodynamic (MHD) equations with large initial velocity and magnetic field slowly varying in one space variable. By means of the anisotropic Littlewood–Paley analysis we prove the global well-posedness of solutions in the framework of anisotropic type Besov spaces for ϵ and σ sufficiently small. Toward this and due to the divergence-free property of magnetic field, the proof is base...
Source: Nonlinear Analysis: Real World Applications - November 29, 2019 Category: Research Source Type: research

Eco-epidemiological model with fatal disease in the prey
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): David Greenhalgh, Qamar J.A. Khan, Fatma Ahmed Al-KharousiAbstractWe investigate a model consisting of a predator population and both susceptible and infected prey populations. The predator can feed on either prey species but instead of choosing individuals at random the predator feeds preferentially on the most abundant prey species. More specifically we assume that the likelihood of a predator catching a susceptible prey or an infected prey is proportional to the numbers of these two different types of prey species. This p...
Source: Nonlinear Analysis: Real World Applications - November 29, 2019 Category: Research Source Type: research

Large time behaviors of solutions to the unipolar hydrodynamic model of semiconductors with physical boundary effect
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Hui Sun, Ming Mei, Kaijun ZhangAbstractIn this paper, we study the asymptotic behaviors in time of solutions to the unipolar hydrodynamic model of semiconductors in the form of Euler–Poisson equations on the half line with the boundary effect, where the boundary conditions are proposed physically as the inflow/outflow/impermeable boundary or the insulating boundary. Different from the Cauchy problem, the boundary effect causes some essential difficulties in determining the asymptotic profiles for the solutions and occurs t...
Source: Nonlinear Analysis: Real World Applications - November 29, 2019 Category: Research Source Type: research

Coexistence of the solitary and periodic waves in convecting shallow water fluid
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Xianbo Sun, Wentao Huang, Junning CaiAbstractThe existence of a solitary wave for the shallow water model in convecting circumstance was established in previous works. It is still unknown that whether there exist periodic waves. In this paper, we prove that the models possess periodic waves with a fixed range of wave speed. The amplitude and wave speed are explicitly given. Moreover, the coexistence of the solitary wave and one periodic wave is established. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - November 25, 2019 Category: Research Source Type: research

Global regularity of 2D generalized MHD equations with magnetic damping
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Caochuan Ma, Zhaoyun ZhangAbstractIn this paper, we focus on the global regularity of 2D generalized magnetohydrodynamics equations with magnetic damping |b|β−1b. Basing on the Maximal regularity of parabolic equation, we are able to show that this system has global smooth solutions when the initial data is sufficiently smooth. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - November 22, 2019 Category: Research Source Type: research

Stationary solutions to outflow problem for 1-D compressible fluid models of Korteweg type: Existence, stability and convergence rate
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Hakho HongAbstractIn this paper, we are concerned with the outflow problem in the half line (0,∞) to the isothermal compressible Navier–Stokes–Korteweg system with a nonlinear boundary condition for vanishing capillary tensor at x=0. We first give some necessary and sufficient conditions for the existence of the stationary solutions with the aid of center manifold theory. We also show the stability of the stationary solutions under smallness assumptions on the initial perturbation in the Sobolev space, by employing an ...
Source: Nonlinear Analysis: Real World Applications - November 20, 2019 Category: Research Source Type: research

Dynamics of a waterborne pathogen model with spatial heterogeneity and general incidence rate
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Yu Yang, Lan Zou, Jinling Zhou, Cheng-Hsiung HsuAbstractThis paper is concerned with the dynamics of a waterborne pathogen model with spatial heterogeneity and general incidence rate. We first establish the well-posedness of this model. Then we clarify the relationship between the local basic reproduction number R̃ and the basic reproduction number R0. It could be seen that R0 plays an important role in determining the global dynamics of this model. In fact, we show that the disease-free equilibrium is globally asymptotical...
Source: Nonlinear Analysis: Real World Applications - November 16, 2019 Category: Research Source Type: research

Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Meina SunAbstractThe analytical solutions of the Riemann problem for the isentropic Euler system with the logarithmic equation of state are derived explicitly for all the five different cases. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is shown that the solution consisting of two shock waves converges to a delta shock wave solution as well as the solution consisting of two rarefaction waves converges to a solution consisting of fo...
Source: Nonlinear Analysis: Real World Applications - November 16, 2019 Category: Research Source Type: research

Global stability of rarefaction waves for a viscous radiative and reactive gas with temperature-dependent viscosity
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Yongkai LiaoAbstractWe study the nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional viscous radiative and reactive gas when the viscosity and heat conductivity coefficients depend on both density and absolute temperature. Our main idea is to use the smallness of the strength of the rarefaction waves to control the possible growth of its solutions induced by the nonlinearity of the system and the interactions of rarefaction waves from different families. The proof is based on some detailed ana...
Source: Nonlinear Analysis: Real World Applications - November 14, 2019 Category: Research Source Type: research

A free boundary tumor model with time dependent nutritional supply
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Wenlong Sun, Tomás Caraballo, Xiaoying Han, Peter E. KloedenAbstractA non-autonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion equation describing the distribution of vital nutrients in the tumor and a nonlinear integro-differential equation describing the evolution of the tumor size. First the global existence and uniqueness of a transient solution is established under some general conditions. Then with additional regularity assumptions on the consumption and prol...
Source: Nonlinear Analysis: Real World Applications - November 13, 2019 Category: Research Source Type: research

The global existence and asymptotic stability of solutions for a reaction–diffusion system
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Samir Bendoukha, Salem Abdelmalek, Mokhtar KiraneAbstractThis paper studies the solutions of a reaction–diffusion system with nonlinearities that generalize the Lengyel–Epstein and FitzHugh–Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the solutions. Furthermore, we present some numerical examples. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - November 11, 2019 Category: Research Source Type: research

Modeling eating disorders in young people
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Andrea Giacobbe, Giuseppe Mulone, Wendi WangAbstractA mathematical model is proposed to simulate the eating disorders of bulimia or anorexia. Earlier models are extended to incorporate the body mass index, which plays a key role in the eating attitude of self thinners. The global existence and ultimate boundedness of solutions of the nonlocal model are proved by using estimates of solutions. The basic reproduction number of eating disorder contagion is shown to be the invasion threshold. The testable linear and nonlinear sta...
Source: Nonlinear Analysis: Real World Applications - November 8, 2019 Category: Research Source Type: research

Editorial Board
Publication date: April 2020Source: Nonlinear Analysis: Real World Applications, Volume 52Author(s): (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - November 5, 2019 Category: Research Source Type: research

On the global dynamics and integrability of the Chemostat system
We describe its global dynamics on the Poincaré disc and study its Liouvillian integrability. For the first topic we use the well-known Poincaré compactification theory and for the second one we make use of the Puiseux series to derive the structure of all the irreducible invariant algebraic curves. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - October 24, 2019 Category: Research Source Type: research

Invariant manifolds of Competitive Selection–Recombination dynamics
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Stephen Baigent, Belgin SeymenoğluAbstractWe study the two-locus-two-allele (TLTA) Selection–Recombination model from population genetics and establish explicit bounds on the TLTA model parameters for an invariant manifold to exist. Our method for proving existence of the invariant manifold relies on two key ingredients: (i) monotone systems theory (backwards in time) and (ii) a phase space volume that decreases under the model dynamics. To demonstrate our results we consider the effect of a modifier gene β on a primary ...
Source: Nonlinear Analysis: Real World Applications - October 24, 2019 Category: Research Source Type: research