相关论文: Traveling waves and spreading speeds for time-spac…

In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…

In this paper, we shall establish the spreading speed and existence of traveling waves for a non-cooperative system arising from epidermal wound healing and characterize the spreading speed as the slowest speed of a family of non-constant…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

This paper presents results on the unboundedness and minimal speed of traveling wave solutions for a one-dimensional spatial reaction-diffusion equation with an asymptotically linear reaction term and a saturation parameter. By applying a…

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows.…

In this article, we are interested in a non-monotone system of logistic reaction-diffusion equations. This system of equations models an epidemics where two types of pathogens are competing, and a mutation can change one type into the other…

In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…

This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…

In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct…

This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover…

It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301 (2002)]. As a further investigation, here we observe different types of traveling…

We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…

This paper focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic…

This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us…

This paper is devoted to the study of propagation dynamics for a large class of non-monotone evolution systems. In two directions of the spatial variable, such a system has two limiting systems admitting the spatial translation invariance.…

In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence…

In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau-Korteweg de Vries equation. We establish existence as well as linear…

Many systems in life sciences have been modeled by reaction-diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events,…

This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…