相关论文: Travelling waves for the cane toads equation with …
We are concerned with travelling wave solutions arising in a reaction diffusion equation with bistable and nonlocal nonlinearity, for which the comparison principle does not hold. Stability of the equilibrium $u\equiv 1$ is not assumed. We…
We investigate the asymptotic speed of spread of the solutions of a non-autonomous Fisher-KPP equation with nonlocal diffusion, driven by a thin-tailed kernel. In this paper, we are concerned with both compactly supported and exponentially…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
We address the uniqueness of the nonzero stationary state for a reaction-diffusion system of Fisher-KPP type that does not satisfy the comparison principle. Although the uniqueness is false in general, it turns out to be true under…
We investigate exact travelling wave solutions of higher order nonlinear Schrodinger equation in the absence of third order dispersion, which exhibit non-trivial self phase modulation. It is shown that, the corresponding dynamical equation,…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially…
We prove the existence and uniqueness, up to a shift in time, of curved traveling fronts for a reaction-advection-diffusion equation with a combustion-type nonlinearity. The advection is through a shear flow $q$. This analyzes, for…
The notion of traveling wave, which typically refers to some particular spatio-temporal con- nections between two stationary states (typically, entire solutions keeping the same profile's shape through time), is essential in the…
This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
We obtain the precise decay rates of traveling wave for a class of nonlocal evolution equations arising in the theory of phase transitions. We also investigate the spectrum of the operator obtained by linearizing at such a traveling wave.…
In this paper we study the existence of traveling wave solutions for a free-boundary problem modeling the phase transition of a material where the heat is transported by both conduction and radiation. Specifically, we consider a…
Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…
Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective…
We consider several non-local models for traffic flow, including both microscopic ODE models and macroscopic PDE models. The ODE models describe the movement of individual cars, where each driver adjusts the speed according to the road…
A modification of the parabolic Allen-Cahn equation, determined by the substitution of Fick's diffusion law with a relaxation relation of Cattaneo-Maxwell type, is considered. The analysis concentrates on traveling fronts connecting the two…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
We consider the reaction-diffusion equation \begin{equation*} u_t=u_{xx}+\mu\left(\int_\Omega M(y,z)u(t,x,z)dz-u\right) + u\left(a(y)-\int_\Omega K(y,z) u(t,x,z)dz\right) , \end{equation*} where $ u=u(t,x,y) $ stands for the density of a…
This paper investigates the stability of interfacial long waves in two-layer plane Couette flow using a nonlinear, nonlocal asymptotic model derived from the Navier-Stokes equations and valid for thin upper layers. Nonlocality enters…