相关论文: Super-linear spreading in local and non-local cane…

It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In…

Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…

In this paper we study the asymptotic nonlinear dynamics of scalar semilinear parabolic problems reaction-diffusion type when the diffusion coefficient becomes large in a subregion which is interior to the domain. We obtain, under suitable…

We study transport in a one-dimensional lattice system with two conserved quantities -- `volume' and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate…

We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the…

We consider the well-posedness of models involving age structure and non-linear diffusion. Such problems arise in the study of population dynamics. It is shown how diffusion and age boundary conditions can be treated that depend…

In this paper we consider a model for the diffusion of a population in a strip-shaped field, where the growth of the species is governed by a Fisher-KPP equation and which is bounded on one side by a road where the species can have a…

We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi two-dimensional reaction-diffusion equation can be reduced…

We present a general, physically motivated non-linear and non-local advection equation in which the diffusion of interacting random walkers competes with a local drift arising from a kind of peer pressure. We show, using a mapping to an…

We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…

We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue…

We introduce and study a class of free boundary models with "nonlocal diffusion", which are natural extensions of the free boundary models in Du and Lin [17] and elsewhere, where "local diffusion" is used to describe the population…

In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…

We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic…

We investigate the influence of a shifting environment on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is homogeneous and favourable, this model was…

We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…

In this article, we perform an asymptotic analysis of a nonlocal reaction-diffusion equation, with a fractional laplacian as the diffusion term and with a nonlocal reaction term. Such equation models the evolutionary dynamics of a…

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…

We study scaling properties of energy spreading in disordered strongly nonlinear Hamiltonian lattices. Such lattices consist of nonlinearly coupled local linear or nonlinear oscillators, and demonstrate a rather slow, subdiffusive spreading…

This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…