We consider a singular limit for the compressible Navier–Stokes system with general non-monotone pressure law in the asymptotic regime of low Mach number and large Reynolds numbers. We show that any dissipative weak solution approaches the solution of incompressible Euler equation both for well-prepared initial data and ill-prepared initial data.

This paper is devoted to the Neumann problem of a stationary Lotka–Volterra model with diffusion and advection. In the model it is assumed that one population growth rate is described by weak Allee effect. We first obtain some sufficient conditions ensuring the existence of nonconstant solutions by using the Leray–Schauder degree theory. And then we study a limiting system (with nonlocal constraint)

We consider the inhomogeneous biharmonic nonlinear Schrödinger equation (IBNLS) iut+Δ2u+λ|x|−b|u|αu=0, where λ=±1 and α, b>0. We show local and global well-posedness in Hs(RN) in the Hs-subcritical case, with s=0,2. Moreover, we prove a stability result in H2(RN), in the mass-supercritical and energy-subcritical case. The fundamental tools to prove these results are the standard Strichartz estimates

Pyroptosis is a highly inflammatory form of cell death, which uses intracellularly generated pores to destroy electrolyte homeostasis and perform cell death. Gasdermin D, the pore-forming effector protein of pyroptosis, plays a critical role in coordinating membrane lysis and the release of highly inflammatory molecules. Recently, necrosulfonamide as a direct chemical inhibitor of gasdermin D has been

In this paper, we investigate a Lotka–Volterra competition model with Danckwerts boundary conditions in a one-dimensional habitat where one species assumes pure random diffusion while another one undergoes mixed movement (both random and directed movements). We focus on the joint influence of advection rate, intrinsic growth rate and interspecific competition coefficient on the competition outcomes

We investigate the stability of the Rayleigh–Taylor (RT) problem for stratified viscoelastic fluids with internal surface tension. More precisely, under the stability condition Dis(ϑ,κ)<1, we prove the existence of unique strong solution with exponential decay in time for the (stratified) viscoelastic RT (VRT) problem with proper initial data in Lagrangian coordinates. This shows that a sufficiently

This paper deals with the 2D incompressible Navier–Stokes equations with density-dependent viscosity over bounded domains. The global existence of strong solutions is established in the vacuum cases, provided the assumption that the bound of density is suitably small, which is in sharp contrast to the recent work (Huang and Wang, 2014), where the smallness assumption on ‖∇μ(ρ0)‖Lq(q>2) is needed. Furthermore

This article is concerned about the synchronization problem of the bidirectionally coupled Kuramoto model. In this model, each oscillator only interacts with the oscillators with adjacent labeling numbers. Namely, the oscillator θi only interacts with θi+1 and θi−1. In real applications, this is a typical setting of concatenation connection. We first prove the global convergence of frequency synchronization

We study the homogeneous Dirichlet problem for a class of nonlocal singular parabolic equations ut−div|∇u|p[u]−2∇u=fin Ω×(0,T),where Ω⊂Rd, d≥2, is a smooth bounded domain, p[u]=p(l(u)) is a given function with values in the interval [p−,p+]⊂(1,2), and l(u)=∫Ω|u(x,t)|αdx, α∈[1,2], is a functional of the unknown solution. We find sufficient conditions for global or local in time solvability of the problem

This paper is concerned about the S–K–T competition model with spatially heterogeneous interactions, in which the two competing species are identical in all aspects except for their interspecific competitions. Under small variations of interspecific competitions, a good understanding of the dynamics and the structure of the set of steady states is gained by the Lyapunov–Schmidt procedure and detailed

A new kind of model based on double degenerate parabolic equation in nondivergence form is proposed for multiplicative noise removal. We first utilize the regularization method to illustrate the existence of the weak solution for the problem and the non-expansion of support of the solution is also provided. In the numerical aspect, experiments and comparisons with other denoising models are presented

In this paper, we consider an age-structured population model with diffusion. We first establish a comparison principle. We then apply the comparison principle to show the existence and uniqueness of solutions by constructing monotone sequences of weak upper and lower solutions. We also use the comparison principle to study the long-time behavior of the solution and present extinction and boundedness

The zero dissipation limit of the one-dimensional non-isentropic micropolar equations is studied in this paper. If the given rarefaction wave which connects to vacuum at one side, a sequence of solution to the micropolar equations can be constructed which converge to the above rarefaction wave with vacuum as the viscosity and the heat conduction coefficient tend to zero. Moreover, the uniform convergence

We introduce a model of the growth of a single microorganism in a self-cycling fermentor in which an arbitrary number of resources are limiting, and impulses are triggered when the concentration of one specific substrate reaches a predetermined level. The model is in the form of a system of impulsive differential equations. We consider the operation of the reactor to be successful if it cycles indefinitely

In this paper we study the chemotaxis–Stokes system with slow p-Laplacian diffusion and rotation: nt+u⋅∇n=∇⋅(|∇n|p−2∇n)−∇⋅(nS(x,n,c)⋅∇c), ct+u⋅∇c=Δc−nc, ut+∇P=Δu+n∇ϕ+f(x,t) and ∇⋅u=0 in a bounded domain Ω⊂R3 with p>2, subject to the Neumann–Neumann–Dirichlet boundary conditions, where ϕ:Ω̄→R, f:Ω̄×[0,∞)→R3 and S:Ω̄×[0,∞)2→R3×3 are given sufficiently smooth functions with f bounded in Ω×(0,∞), |S(x

We provide sufficient conditions for the existence of periodic solutions of the Lorentz force equation, which models the motion of a charged particle under the action of an electromagnetic fields. The basic assumptions cover relevant models with singularities like Coulomb-like electric potentials or the magnetic dipole.

Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. The results are applied to a population model with fishing, and to the existence and stability of limit cycles. We also describe in detail our numerical computations of curves of periodic solutions, and of limit cycles.

Our main goal in the present work is to address an integro-differential model under localized viscoelastic and frictional effects arising in the Boltzmann theory of viscoelasticity. More precisely, we consider a general version in the history context of the pioneer localized viscoelastic problem approached by Cavalcanti and Oquendo (2003) in the null history scenario, and more recently by Cavalcanti

We study a class of Kolmogorov systems of dimension two depending on two independent parameters. The local behavior of the system is described in terms of bifurcation diagrams which contain the bifurcation curves separating a node from a focus.

In this paper, we study a chemotaxis-consumption system with signal-dependent motility and generalized logistic source in a smooth bounded domain. We show that if α>0, ρ∈R, μ>0 and l>maxn+22,2, then for all sufficiently smooth initial data the system ut=Δ(uv−α)+ρu−μul,x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0,possesses a unique global-in-time solution.

In the paper Koch et al. (2009), the authors make the following conjecture: any bounded ancient mild solution of the 3D axially symmetric Navier–Stokes equations is constant. And it is proved in the case that the solution is swirl free. Our purpose of this paper is to improve their result by allowing that the solution can grow with a power smaller than 1 with respect to the distance to the origin.

In this paper, we study a class of semilinear p(x)-Laplacian equations with variable exponent sources. By using potential well method, we first prove a threshold results on the existence and nonexistence of global solutions to the equations when initial energy is less than the mountain pass level d. In the former case we also show the decay properties of energy functional. We finally obtain the non-global

This paper deals with planar piecewise linear refracting systems with a straight line of separation. Using the Poincaré compactification, we provide the classification of the phase portraits in the Poincaré disc of piecewise linear refracting systems with focus-saddle dynamics.

This article is concerned with the mathematical analysis of models for Micro-Electro-Mechanical Systems (MEMS). These models arise in the form of coupled partial differential equations with a moving boundary. Although MEMS devices are often operated in non-isothermal environments, temperature is often neglected in the mathematical investigations. In light of this finding the focus of our modelling

In this study, we consider a directed–diffusion system describing the interactions between two organisms in heterogeneous environment. We first establish a linearly stability of the co-existence (positive) steady state. Then we further present a classification on all possible long-time dynamical behaviors by appealing to the theory of monotone dynamical systems.

Compressible Euler equations with Coriolis force are the fundamental model in the study of atmospheric dynamics. In this article, we study the lifespan of the projected 2-dimensional C2 non-vacuum solutions of the compressible Euler equations with Coriolis force. We first locate the vortex equations for the compressible Euler equations with Coriolis force and then use the integration method to prove

In this paper we establish the existence of at least one smooth positive solution for a singular quasilinear elliptic system involving gradient terms. The approach combines the sub-supersolutions method and Schauder’s fixed point theorem.

We show the following extension of the recent optimal regularity results by Kukavica & Ziane, Cao and Zhang: If u is a solution of the Navier–Stokes equations in the whole space R3 and ∂3u∈Lp(0,T;Lq(R3)), T>0, where 2∕p+3∕q=2 and q∈(3∕2,3], then u is regular on (0,T].

A general seasonally-varying predator–prey model with Allee effect in the prey growth is investigated. The analysis is performed only on the basis of some properties determining the shape of the prey growth rate and the functional responses. General conditions for coexistence are determined, both in the case of weak and strong Allee effect. Finally, a modified Leslie–Gower predator–prey model with

We investigate existence, multiplicity and qualitative properties of the solutions of the Dirichlet problem for the singularly perturbed prescribed mean curvature equation −(1−bu)div(∇u1+|∇u|2)=a(u−R)2+b1+|∇u|2,inΩ,u=0,on∂Ω,where a,b,R are given constants and Ω is a bounded regular domain in RN. This model appears in the theory of micro-electro-mechanical systems (MEMS) when the effects of capillarity

In this paper, we consider an Ostrovsky type equation that includes the regularized short pulse, the Korteweg–deVries and the modified Korteweg–deVries ones. We prove the well-posedness of the solutions for the Cauchy problem associated with these equations.

In this paper, we consider the equations of stationary motion of electrorheological fluids in any dimension n≥2. We show that the first gradient of local solutions to the system has optimal Lq-regularity with some q>1 with respect to the one of the external force. This is achieved by comparison principle and a good λ-estimate.

This paper proposes an ω-periodic version of the Ellermeyer model of delayed chemostat. We obtain a sufficient condition ensuring the existence of a positive ω-periodic solution. Our proof is based on the application of the generalized continuation theorem. In addition, as a consequence of the implicit function theorem, we obtain a uniqueness result for sufficiently small delays.

In this work, we present a new mathematical model of a boundary coupled neuron network described by the partly diffusive Hindmarsh–Rose equations. We prove the global absorbing property of the solution semiflow and then the main result on the asymptotic synchronization of this neuron network at a uniform exponential rate provided that the boundary coupling strength and the stimulating signal exceed

In this paper, we propose and study the dynamics of a non-autonomous biocontrol model concerned with native consumer A, biocontrol agent B and their common predator L. We assume that some parameters in our proposed model are nonnegative functions instead of being bounded below by positive reals. This assumption is more realistic but makes mathematical proofs more challenging. We first study the positive

This paper deals with a reaction–diffusion system modeling predator–prey interaction with additive Allee effect. We first analyze nonnegative constant equilibrium solutions and study the stability of the unique positive solution. Then we investigate the steady state bifurcation and Hopf bifurcation from the unique positive constant solution, respectively. The main tools used here include the bifurcation

We prove existence of global in time strong solutions for the system of equations modelling nonstationary flows of variable density incompressible asymmetric fluids in 3-dimensional thin domains of the form Ω=defR2×(0,ϵ), where 0<ϵ≤1. Moreover, we show that, when ϵ→0+, the linear and angular velocities tend to vanish away from the initial time.

We investigate nodal radial solutions to semilinear problems of type −Δu=f(|x|,u)inΩ,u=0on∂Ω,where Ω is a bounded radially symmetric domain of RN (N≥2) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions

We consider the time-dependent Landau–Lifshitz–Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and the Dzyaloshinskii–Moriya interaction (which accounts

We consider a Robin problem driven by a nonlinear, nonhomogeneous differential operator and a reaction term which depends on the gradient. Using a topological approach based on the Leray–Schauder Alternative Principle, we show the existence of a weak solution.

We consider mathematical modeling of problems with free boundaries, namely, the investigation of the Stefan type problem with a non-constant melting point, taking into account the pressure in the liquid phase. A mathematical model has been constructed that describes the melting process of heavy paraffin-base crude oil. We prove an existence and uniqueness of a solution of a Stefan-type problem in the

This paper applies a delicate method which is inspired by Deuring (1987) and is different from those of Winkler (2010) and Yang et al. (2015) to show the known conclusion: The weak chemotactic effect can ensure the global existence and boundedness of the solutions of the minimal Keller–Segel model with logistic growth in any dimensional cases. Moreover, we obtain the explicit uniform-in-time upper

We consider the decay rate of Timoshenko type equations for beams with complementary frictional damping and memory effect in an interval. Under only basic conditions on the memory kernels (without any decaying conditions), we show that the solution energy of Timoshenko systems decays uniformly at the rate t−1. Simultaneously, the same rate is also obtained for the corresponding single memory-dissipative

This work is devoted to the time periodic traveling wave phenomena of a generalization of the classical Kermack–McKendrick model with seasonality and nonlocal interaction derived by mobility of individuals during latent period of disease. When the basic reproduction number R0 is bigger than 1, we find a critical value c∗ and prove the existence of periodic traveling waves with the wave speed c>c∗.

This paper deals with the following nonlinear equations Mλ,Λ±(D2u)+g(u)=0inRN,where Mλ,Λ± are the Pucci’s extremal operators, for N⩾1 and under the assumption g′(0)>0. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. Moreover these solutions are periodic, if N=1, while they are radial symmetric and decay to zero at infinity with their derivatives, if N⩾2.

In this paper, we consider an SIS epidemic reaction–diffusion model with spontaneous infection and logistic source in a heterogeneous environment. The uniform bounds of solutions are established, and the global asymptotic stability of the constant endemic equilibrium is discussed in the case of homogeneous environment. This paper aims to analyze the asymptotic profile of endemic equilibria (when it

Oncolytic virotherapy (OVT) is a promising therapeutic approach that uses replication-competent viruses to target and kill tumor cells. Alphavirus M1 is a selective oncolytic virus which showed high efficacy against tumor cells. Wang et al. (2016) studied an ordinary differential equation (ODE) model to verify the potent efficacy of M1 virus. Our purpose is to extend their model to include the effect

In this paper we discuss a model of allelopathy and bacteriocin in the chemostat with a wild-type organism and a single mutant. Dynamical properties of this model show the basic competition between two microorganisms. A qualitative analysis about the boundary equilibrium, a state that microorganisms both vanish, is carried out. The existence and uniqueness of the interior equilibrium are proved by

Analytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative features as the corresponding local models. In particular, using the introduced notion of the stability in the mean integral sense we prove the competitive exclusion