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Qualitative properties of pulsating fronts for reaction–advection–diffusion equations in periodic excitable media Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210916
ZhenHui Bu, JunFeng HeIn this paper, we study the pulsating fronts of reaction–advectiondiffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed

Pullback attractors for a critical degenerate wave equation with timedependent damping Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210915
Dandan Li, Qingquan Chang, Chunyou SunThe aim of this paper is to analyze the longtime dynamical behavior of the solution for a degenerate wave equation with timedependent damping term ∂ttu+β(t)∂tu=Lu(x,t)+f(u) on a bounded domain Ω⊂RN with Dirichlet boundary conditions. Under some restrictions on β(t) and critical growth restrictions on the nonlinear term f, we will prove the local and global wellposedness of the solution and derive

Turing instability of the periodic solutions for the diffusive Sel’kov model with saturation effect Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210915
Pu Wang, Yanbin GaoIn this paper, we are concerned with the Turing instability of the spatially homogeneous Hopf bifurcating periodic solutions for the diffusive Sel’kov model with saturation effect. By using the center manifold theorem, normal form theory and the regularly perturbed theory, we derive a formula in terms of the diffusion rates to determine the Turing instability of the spatially homogeneous Hopf bifurcating

Linearizability of planar polynomial Hamiltonian systems Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210914
Barbara Arcet, Jaume Giné, Valery G. RomanovskiIsochronicity and linearizability of twodimensional polynomial Hamiltonian systems are revisited and new results are presented. We give a new computational procedure to obtain the necessary and sufficient conditions for the linearization of a polynomial system. Using computer algebra systems we provide necessary and sufficient conditions for linearizability of Hamiltonian systems with homogeneous

Two solutions for a singular elliptic equation with critical growth at infinity Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210914
Marcelo F. Furtado, Karla Carolina V. de SousaWe look for positive solutions for the singular equation −Δu−12x⋅∇u=μh(x)uq−1+λu+u(N+2)/(N−2),in RN, where N≥3, λ>0, μ>0 is a parameter, 00 is small.

Nonuniform dependence for higher dimensional Camassa–Holm equations in Besov spaces Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210911
Jinlu Li, Wei Deng, Min LiIn this paper, we investigate the dependence on initial data of solutions to higher dimensional Camassa–Holm equations. We show that the datatosolution map is not uniformly continuous dependence in Besov spaces.

Gevrey regularity and finite time singularities for the Kakutani–Matsuuchi model Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210909
Hantaek Bae, Woojae Lee, Jaeyong ShinIn this paper, we deal with the Kakutani–Matsuuchi model which describes the surface elevation η of the waterwaves under the effect of viscosity. We first derive the decay rate of weak solutions. This can be used to obtain the decay rate of ‖η(t)‖Ḣ1 when initial data is sufficiently small in Ḣ1. We next show the existence, uniqueness, Gevrey regularity and decay rates of η with sufficiently small

Minimum energy with infinite horizon: From stationary to nonstationary states Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210910
P. Acquistapace, F. GozziWe study a nonstandard infinite horizon, infinite dimensional linear–quadratic control problem arising in the physics of nonstationary states (see e.g. Bertini et al. (2004, 2005)): finding the minimum energy to drive a given stationary state x̄=0 (at time t=−∞) into an arbitrary nonstationary state x (at time t=0). This is the opposite to what is commonly studied in the literature on null controllability

Global existence and time decay of the noncutoff Boltzmann equation with hard potential Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210907
Hao Wang, Zhendong FangThis paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces HN(Rx,v6) with N≥2. But if we want to obtain the optimal temporal decay estimates, we need to add

Global wellposedness and inviscid limits of the generalized Oldroyd type models Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210908
Xiaoping Zhai, Yuanyuan Dan, Yongsheng LiWe obtain the global small solutions to the generalized OldroydB model without damping on the stress tensor in Rn. Our result give positive answers partially to the question proposed by Elgindi and Liu (Remark 2 in Elgindi and Liu (2015)). The proof relies heavily on the trick of transferring dissipation from u to τ, and a new commutator estimate which may be of interest for future works. Moreover

Decay rates of energy of the 1D damped original nonlinear wave equation Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210903
Weijiu LiuWe consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This

Asymptotic stability of viscous contact wave for the inflow problem of the heatconductive ideal gas without viscosity Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210827
Meichen Hou, Lili FanThis paper is devoted to studying the inflow problem governed by the nonviscous and heatconductive gas dynamic system in the onedimensional half space. We establish the unique globalintime existence and the asymptotic stability of the viscous contact wave. The contact discontinuity in the linearly degenerate field is less stable, and the dissipative mechanism for nonviscous systems is also weaker

Temporal decays and asymptotic behaviors for a Vlasov equation with a flocking term coupled to incompressible fluid flow Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210827
YoungPil Choi, Kyungkeun Kang, Hwa Kil Kim, JaeMyoung KimWe are concerned with largetime behaviors of solutions for Vlasov–Navier–Stokes equations in two dimensions and Vlasov–Stokes system in three dimensions including the effect of velocity alignment/misalignment. We first revisit the largetime behavior estimate for our main system and refine assumptions on the dimensions and a communication weight function. In particular, this allows us to take into

Global existence of bounded solutions to the relativistic BGK model Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210825
ByungHoon HwangThe relativistic BGK model is a representative relaxationtime approximation of the relativistic Boltzmann equation. In this paper, we prove the global existence of bounded solutions to the relativistic BGK model proposed by Anderson and Witting when the initial data satisfies the excess conservations of mass and energy, and the excess entropy inequality from global equilibrium. The L∞ estimate established

A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a nearclogging scenario Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210824
Michael Eden, Christos Nikolopoulos, Adrian MunteanWe study the weak solvability of a macroscopic, quasilinear reaction–diffusion system posed in a 2D porous medium which undergoes microstructural problems. The solid matrix of this porous medium is assumed to be made out of circles of notnecessarily uniform radius. The growth or shrinkage of these circles, which are governed by an ODE, has direct feedback to the macroscopic diffusivity via an additional

Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210824
Debayan Maity, JeanPierre Raymond, Arnab RoyWe study the wellposedness of a system of onedimensional partial differential equations modeling blood flows in a network of vessels with viscoelastic walls. We prove the existence and uniqueness of maximal strong solution for this type of hyperbolic/parabolic model. We also prove a stability estimate under suitable nonlinear Robin boundary conditions.

Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210814
M.R. Batista, J.C. Da Mota, R.A. SantosCombustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a onedimensional nonlinear hybrid system consisting of n reaction–diffusion–convection equations coupled with n ordinary differential equations, which models a combustion front moving through a porous medium with n parallel layers. The state variables

Smallsignal solutions of a twodimensional doubly degenerate taxis system modeling bacterial motion in nutrientpoor environments Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210814
Michael WinklerThe doubly degenerate nutrient taxis model ut=∇⋅(uv∇u)−∇⋅(u2v∇v)+ℓuv,x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0,is considered in smoothly bounded convex subdomains of the plane, with ℓ≥0. It is shown that for any p>2 and each fixed nonnegative u0∈W1,∞(Ω), a smallness condition exclusively involving v0 can be identified as sufficient to ensure that an associated noflux type initial–boundary value problem with (u,v)t=0=(u0

Blowup in a quasilinear parabolic–elliptic Keller–Segel system with logistic source Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210810
Yuya TanakaThis paper deals with the quasilinear parabolic–elliptic Keller–Segel system with logistic source, ut=Δ(u+1)m−χ∇⋅(u(u+1)α−1∇v)+λ(x)u−μ(x)uκ,x∈Ω,t>0,0=Δv−v+u,x∈Ω,t>0,where Ω≔BR(0)⊂Rn(n≥3) is a ball with some R>0; m>0, χ>0, α>0 and κ≥1; λ and μ are continuous nonnegative functions. About this problem, Winkler (2018) found the condition for κ such that solutions blow up in finite time when m=α=1.

Solitary waves of a generalized Ostrovsky equation Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210809
Amin Esfahani, Steven LevandoskyWe consider the existence and stability of traveling waves of a generalized Ostrovsky equation (ut−βuxxx−f(u)x)x=γu, where the nonlinearity f(u) satisfies a powerlike scaling condition. We prove that there exist ground state solutions which minimize the action among all nontrivial solutions and use this variational characterization to study their stability. We also introduce a numerical method for

Energy conservation for the weak solutions to the ideal inhomogeneous magnetohydrodynamic equations in a bounded domain Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210806
Zhipeng ZhangIn this paper, we prove the energy conservation for the weak solutions of the threedimensional ideal inhomogeneous magnetohydrodynamic (MHD) equations in a bounded domain. Two types of sufficient conditions on the regularity of the weak solutions are provided to ensure the energy conservation. Due to the presence of the boundary, we need to impose the boundedness in Lp and the continuity in Lpp−2

Propagation fronts in a simplified model of tumor growth with degenerate crossdependent selfdiffusivity Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210805
Thierry Gallay, Corrado MasciaMotivated by tumor growth in Cancer Biology, we provide a complete analysis of existence and nonexistence of invasive fronts for the reduced Gatenby–Gawlinski model ∂tU=Uf(U)−dV,∂tV=∂xf(U)∂xV+rVf(V),where f(u)=1−u and the parameters d,r are positive. Denoting by (U,V) the traveling wave profile and by (U±,V±) its asymptotic states at ±∞, we investigate existence in the regimes d>1:(U−,V−)=(0,1)and(U+

Optimal decay rate of the twofluid incompressible Navier–Stokes–Fourier–Poisson system with Ohm’s law Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210729
Weihua Gong, Fujun Zhou, Weijun Wu, Qian HuThis paper is to investigate the optimal Lp (p≥2) time decay rate of global solutions to the twofluid incompressible Navier–Stokes–Fourier–Poisson system with Ohm’s law. The result shows that the time decay rate of this system achieves the same as that of the incompressible Navier–Stokes equation, in other words, the coupling of the selfconsistent Poisson equation does not change the decay rate of

Humanvector malaria transmission model structured by age, time since infection and waning immunity Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210726
Quentin Richard, Marc Choisy, Thierry Lefèvre, Ramsès DjidjouDemasseMalaria is one of the most common mosquitoborne diseases widespread in tropical and subtropical regions, causing thousands of deaths every year in the world. Few models considering a multiple structure model formulation including (i) the chronological age of human and mosquito populations, (ii) the time since they are infected, and (iii) humans waning immunity (i.e. the progressive loss of protective

Global and exponential attractors for mixtures of solids with Fourier’s law Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210724
M.M. Freitas, A.J.A. Ramos, D.S. Almeida Júnior, P.T.P. Aum, J.L.L. AlmeidaThis paper presents a study of the longtime dynamics of the dynamical system generated by a nonlinear system modeling mixture of solids with nonlinear damping and Fourier’s law. By using the recent quasistability theory, we prove the existence of a smooth finite dimensional global attractor, which is characterized as an unstable manifold of the set of stationary solutions. The quasistability of

Bifurcation analysis in a diffusive Logistic population model with two delayed densitydependent feedback terms Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210724
XiangPing Yan, CunHua ZhangThe present paper is concerned with a diffusive population model of Logistic type with an instantaneous densitydependent term and two delayed densitydependent terms and subject to the zeroDirichlet boundary condition. By regarding the delay as the bifurcation parameter and analyzing in detail the associated eigenvalue problem, the local asymptotic stability and the existence of Hopf bifurcation

Isobispectral potentials for Sturm–Liouvilletype operators with small delay Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210722
Nebojša Djurić, Sergey ButerinThe paper addresses nonlinear inverse Sturm–Liouvilletype problems with constant delay. Since many processes in the real world possess nonlocal nature, operators with delay as well as other classes of nonlocal operators are continuously finding numerous applications in the natural sciences and engineering. However, in spite of a large number of works devoted to inverse problems for operators with

Large time behavior in a fractional chemotaxis–Navier–Stokes system with logistic source Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210722
Yuzhu Lei, Zuhan Liu, Ling ZhouThis paper deals with a coupled chemotaxis–Navier–Stokes system with logistic source and a fractional diffusion of order α∈(12,1) nt+u⋅∇n=−(−Δ)αn−χ∇⋅(n∇c)+an−bn2,ct+u⋅∇c=Δc−nc,ut+(u⋅∇)u=Δu+∇P+n∇ϕ+f,∇⋅u=0on three dimensional periodic torus T3. Since there is no classical solution in the threedimensional full Navier–Stokes equations, our main purpose of this paper is to investigate the global existence

A note on “Existence and uniqueness of coexistence states for an elliptic system coupled in the linear part”, by Hei Lijun, Nonlinear Anal. Real World Appl. 5, 2004 Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210719
Léo GirardinIn this short paper I report on a paper published in Nonlinear Analysis: Real World Applications in 2004. There is a major mistake early in that paper which makes most of its claims false. The class of reaction–diffusion systems considered in the paper has been the object of a renewed investigation in the past few years, by myself and others, and recent discoveries provide explicit counterexamples

Local wellposedness of Boussinesq equations for MHD convection with fractional thermal diffusion in sobolev space Hs(Rn)×Hs+1−ϵ(Rn)×Hs+α−ϵ(Rn) Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210527
Mohammad GhaniIn this paper, we study the local wellposedness of the Boussinesq equation for MHD convection with fractional thermal diffusion in Hs(Rn)×Hs+1−ϵ(Rn)×Hs+α−ϵ(Rn) with s>n2−1 and any small enough ϵ>0 such that s+1−ϵ>n2 and s+α−ϵ≥s+2−(ϵ+α)>n2. We present here the fractional operator (−Δ)αθ for α>1 which is estimated by using Littlewood–Paley projection.

Exact boundary controllability of partial nodal profile for network of strings Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210716
Yue Wang, Tatsien LiBased on the theory of exact boundary controllability of nodal profile for hyperbolic systems, the authors propose the concept of exact boundary controllability of partial nodal profile to expand the scope of applications. With the new concept, we can shorten the controllability time, save the number of controls, and increase the number of charged nodes with given nodal profiles. Furthermore, we introduce

A dynamical model of echinococcosis with optimal control and costeffectiveness Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210715
Jianglin Zhao, Run YangA dynamical model of echinococcosis transmission with optimal control strategies is first presented. The basic reproduction number of the model is determined and employed to study the global stability of the diseasefree and endemic equilibrium points. The optimal control problem is formulated and solved analytically. Numerical simulations show that optimal control strategies could effectively reduce

Bifurcation of equilibrium forms of a gas column rotating with constant speed around its axis of symmetry Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210715
Joanna Janczewska, Anita ZgorzelskaWe will be concerned with the problem of deformation of the lateral surface of a column that rotates with constant speed around its axis of symmetry. The column is filled by a gas and our goal is to investigate the deformation of the lateral surface depending on the pressure of the gas.

On a Mathematical model for traveling sand dune Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210709
Noureddine Igbida, Fahd Karami, Driss MeskineOur aim in this paper is to introduce and study a mathematical model for the description of traveling sand dunes. We use surface flow process of sand under the effect of wind and gravity. We model this phenomenon by a nonlinear diffusion–transport equation coupling the effect of transportation of sand due to the wind and the avalanches due to the gravity and the repose angle. The avalanche flow is

Asymptotic behavior of nonlinear sound waves in inviscid media with thermal and molecular relaxation Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210708
Vanja Nikolić, Belkacem SaidHouariNonlinear sound propagation through media with thermal and molecular relaxation can be modeled by thirdorder in time wavelike equations with memory. We investigate the asymptotic behavior of a Cauchy problem for such a model, the nonlocal Jordan–Moore–Gibson–Thompson equation, in the socalled critical case, which corresponds to propagation through inviscid fluids or gases. The memory has an exponentially

Global phase portraits of planar piecewise linear refracting systems of saddle–saddle type Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210701
Yi Shao, Shimin Li, Kuilin WuThis paper deal with the global dynamics of planar piecewise linear refracting systems of saddle–saddle type with a straight line of separation. We investigate the singularities, limit cycles, homoclinic orbits, heteroclinic orbits and make the classification of global phase portraits in the Poincaré disk for the refracting systems. We prove that these systems have 18 topologically different global

Some new regularity criteria for the Navier–Stokes equations in terms of one directional derivative of the velocity field Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210701
N.V. Giang, D.Q. KhaiWe establish some regularity criteria for the solutions to the Navier–Stokes equations in the full threedimensional space in terms of one directional derivative of the velocity field. Revising the method used by Zujin Zhang (2018), we show that a weak solution u is regular on (0, T] provided that ∂u∂x3∈Lp(0,T;Lq(R3)) with s=2 for 3≤q≤6, 116

Asymptotic convergence of solutions to the forest kinematic model Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210629
Satoru IwasakiWe study the asymptotic behavior of global solutions to forest kinetic model equations composed of young trees, old trees, and airborne seeds. Under some parameter assumptions, we prove the asymptotic convergence of global solutions to a stationary solution. To this end, we show a nonsmooth version of the Łojasiewicz–Simon gradient inequality on a suitable functional space and a certain norm estimate

Low Mach number limit of the full compressible Hallmagnetohydrodynamic equation with general initial data Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210624
Kaijian Sha, Yeping LiIn this paper, we are concerned with the low Mach number limit for the full compressible Hallmagnetohydrodynamic equations within the frame work of local smooth solution in R3. Under the assumption of large temperature variations, we first obtain the uniform estimates of the solutions in a εweighted Sobolev space, which establishes the local existence theorem of the full compressible Hallmagnetohydrodynamic

Stabilization to a positive equilibrium for some reaction–diffusion systems Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210621
JongShenq Guo, Masahiko ShimojoThe aim of this paper is to study the asymptotic behavior of solutions for some reaction–diffusion systems in biology. First, we establish a Liouville type theorem for entire solutions of these reaction–diffusion systems. Based on this theorem, we derive the stabilization of the solutions of the reaction–diffusion system to the unique positive constant state, under the condition that this positive

Regularity results for solutions to a class of obstacle problems Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210614
Antonio Giuseppe GrimaldiIn this paper we prove some regularity properties of solutions to variational inequalities of the form ∫Ω〈A(x,u,Du),D(φ−u)〉dx≥∫ΩB(x,u,Du)(φ−u)dx,∀φ∈Kψ(Ω).Here Ω is a bounded open set of Rn, n≥2, the function ψ:Ω→[−∞,+∞), called obstacle, belongs to the Sobolev class W1,p(Ω) and Kψ(Ω)={w∈W1,p(Ω):w≥ψq.o. inΩ} is the class of the admissible functions. First we establish a local Calderòn–Zygmund type estimate

Existence of a fundamental solution of partial differential equations associated to Asian options Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210610
Francesca Anceschi, Silvia Muzzioli, Sergio PolidoroWe prove the existence and uniqueness of the fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in the Black & Scholes setting for the pricing problem relevant to path dependent options. We improve previous results in that we provide a closed form expression for the solution of the Cauchy problem under weak regularity assumptions on the coefficients of

On a nonlinear nonlocal model for a population with separate dispersal and sedentary stages Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210608
Keng Deng, Qihua HuangThe life cycles of many species include separate dispersal and sedentary stages. To understand the population dynamics of such species, we study a hybrid model consisting of a reaction–diffusion equation that governs the random movement and settlement of dispersal individuals and an agestructured hyperbolic equation that describes the growth of sedentary individuals. We establish the existence and

Global wellposedness to a chemotaxisStokes system Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210605
Ying Yang, Chunhua JinThis paper concerns the chemotaxisStokes system nt+u⋅∇n=Δnm−∇⋅(n∇c)+μn(1−n),ct+u⋅∇c=Δc−cnα,ut=Δu−∇π+n∇φ,∇⋅u=0in a three dimensional bounded domain under noflux boundary conditions for n,c and noslip boundary conditions for u. The purpose of this paper is to study the global solvability and large time asymptotic behavior of solutions. Here, it is worth mentioning that the nonlinear consumption term

Sobolev hyperbola for periodic Lane–Emden heat flow system in N spatial dimension Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210601
Haochuan Huang, Jingxue Yin, Rui HuangThe wellknown Lane–Emden conjecture indicates that, for the elliptic Lane–Emden system −Δu=vp, −Δv=uq in RN, the Sobolev hyperbola 1p+1+1q+1=N−2N is expected as the critical curve for the existence and nonexistence of entire solutions. In this paper, we study the periodic Lane–Emden heat flow system ut−Δu=a(t)vp, vt−Δv=b(t)uq in a bounded domain Ω of RN, subject to homogeneous Dirichlet boundary condition

Wolbachia spreading dynamics in Nilaparvata lugens with two strains Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210529
Zhigang Liu, Tiejun ZhouThe Nilaparvata lugens is primary vector of rice diseases such as rice ragged stunt. A recent study reported the Wolbachia wStri can cause the cytoplasmic incompatibility of N.lugens, and inhibit the infection and transmission of rice ragged stunt virus in the laboratory. In this work, based on multistrains infection mechanisms including incomplete cytoplasmic incompatibility and imperfect maternal

The impact of Wolbachia on dengue transmission dynamics in an SEI–SIS model Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210527
Yazhi Li, Lili LiuDengue has grown dramatically in recent decades globally. In order to investigate the spread of dengue with vector control, especially, the impact of Wolbachia on dengue transmission, a mathematical model is established and analyzed to study dengue transmission between humans and mosquitoes. Firstly, model qualitative analysis including the existence and local asymptotic stability of denguefree equilibria

Coupling local and nonlocal diffusion equations for image denoising Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210527
Kehan ShiDue to the strong ability of restoring textures and details in images, nonlocal equations have attracted an extensive interest for image denoising. However, the lack of regularity causes residual noise in the restored images. In this paper, we propose and study an evolution equation consisting of the weighted local and the weighted nonlocal pLaplacian equations. The existence and uniqueness of solutions

Energy conservation for the weak solutions to the 3D compressible magnetohydrodynamic equations of viscous nonresistive fluids in a bounded domain Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210527
Xiong Wang, Sili LiuIn this paper, inspired by the work of Chen–Liang–Wang–Xu (Chen et al., 2020) on compressible Navier–Stokes equations, we obtain the energy conservation for weak solutions of the compressible nonresistive magnetohydrodynamic flows in a bounded domain Ω⊂R3. To ensure the energy conservation, we need the same regularity conditions of density and velocity as in Chen et al. (2020), moreover, H∈Lt4Lx4

Global existence of solutions to a parabolic attraction–repulsion chemotaxis system in R2: The attractive dominant case Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210527
Toshitaka Nagai, Yukihiro Seki, Tetsuya YamadaWe discuss the Cauchy problem for the following parabolic attraction–repulsion chemotaxis system: ∂tu=Δu−∇⋅(β1u∇v1)+∇⋅(β2u∇v2),t>0,x∈R2,∂tvj=Δvj−λjvj+u,t>0,x∈R2(j=1,2),u(0,x)=u0(x),vj(0,x)=vj0(x),x∈R2(j=1,2)with constants βj, λj>0 (j=1,2). In this paper we prove that the nonnegative solutions exist globally in time under the assumption (β1−β2)∫R2u0dx<8π in the attractive dominant case β1>β2.

Blowup and lifespan estimates of solutions to semilinear Moore–Gibson–Thompson equations Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210526
Sen Ming, Han Yang, Xiongmei Fan, Jiangyan YaoIn this paper, the blowup of solutions to the Cauchy problems for semilinear Moore–Gibson–Thompson equations with power nonlinearity up, derivative nonlinearity utp, combined nonlinearity utp+uq are investigated. Upper bound lifespan estimates of solutions to the problems in the subcritical and critical cases are also deduced by applying the test function approach. It is worth noticing that

Fujita exponents for a space–time weighted parabolic problem in bounded domains Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210520
Xizheng Sun, Bingchen Liu, Fengjie LiThis paper deals with a semilinear weighted parabolic problem in general bounded domains, subject to zero Dirichlet boundary conditions, where the weighted functions depend not only on space variable but also on time variable. Fujita exponents for blowup and global existence of solutions are determined by using semigroup methods and the comparison principle, which are composed by the dimensions of

Qualitative analysis on an SIRS reaction–diffusion epidemic model with saturation infection mechanism Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210520
Chuanxin Liu, Renhao CuiIn this paper, we deal with an SIRS reaction–diffusion epidemic model with saturation infection mechanism. Based on the uniform boundedness of the parabolic system, we investigate the extinction and persistence of the infectious disease in terms of the basic reproduction number. To better investigate the effects of infection mechanism and individual diffusion, we further analyze the asymptotic profiles

Regularity for obstacle problems without structure conditions Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210514
Giacomo Bertazzoni, Samuele RiccòThis paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurrence of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap is needed. The main tool used here is a crucial Lemma which reveals to be needed because it allows us to move from the variational obstacle

An improved spatially controlled reaction–diffusion equation with a nonlinear second order operator for image superresolution Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210511
Aissam Hadri, Hamza Khalfi, Amine Laghrib, Mourad NachaouiIn this work, we introduce an efficient secondorder reaction–diffusion (R.D.) equation for noise removal and image superresolution. The main idea is to decompose the image into two components: cartoon and texture parts using a new spatially controlled diffusion obtained by incorporating into R.D. equation an antidiffusion effect modelled by a space dependent parameter γ. Hence, the proposed equation

On the stability of the improved Aw–Rascle–Zhang model with Chaplygin pressure Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210511
Tingting Chen, Weifeng Jiang, Tong LiIn this paper, we mainly study the stability of Riemann problem for the improved Aw–Rascle–Zhang model which describes the formation and dynamics of traffic jams. First of all, we construct the classical Riemann solutions by elementary waves with the method of characteristic analysis. With the generalized Rankine–Hugoniot and entropy conditions, we prove the existence and uniqueness of δshock wave

Dynamical boundary problem for DirichlettoNeumann operator with critical Sobolev exponent and Hardy potential Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210511
Yanhua Deng, Zhong Tan, Minghong XieWe study the Laplacian equation with dynamical boundary condition involving DirichlettoNeumann operator, critical growth, and Hardy potential. We first prove the existence and decay estimates of global solutions and finite time blowup of local solutions under certain assumptions. Then we focus on the asymptotic behavior of global solutions approaching a stationary solution in the long time series

Nonexistence of global solutions for generalized Tricomi equations with combined nonlinearity Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210507
Wenhui Chen, Sandra Lucente, Alessandro PalmieriIn the present paper, we investigate the blowup dynamics for local solutions to the semilinear generalized Tricomi equation with combined nonlinearity. As a result, we enlarge the blowup region in comparison to the ones for the corresponding semilinear models with either power nonlinearity or nonlinearity of derivative type. Our approach is based on an iteration argument to establish lower bound

Competitive exclusion in a nonlocal reaction–diffusion–advection model of phytoplankton populations Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210507
Danhua Jiang, KingYeung Lam, Yuan LouWe continue our study on the global dynamics of a nonlocal reaction–diffusion–advection system modeling the population dynamics of two competing phytoplankton species in a eutrophic environment, where both populations depend solely on light for their metabolism. In our previous work, we proved that system (1.1) is a strongly monotone dynamical system with respect to a nonstandard cone related to the

Eigenvalue criteria for semipositone Neumann elliptic problem in exterior domain Nonlinear Anal. Real World Appl. (IF 2.763) Pub Date : 20210505
Filomena Cianciaruso, Paolamaria PietramalaNew criteria are established for the existence of positive solutions of a semipositone elliptic problem on the exterior of a ball in which the Neumann boundary conditions are non local. These criteria are determined by the relationship between the behaviour of the nonlinearity as the variable tends to 0 or ∞ and the principal (positive) eigenvalue of a suitable associate linear Hammerstein integral