Dynamical behavior of a temporally discrete non-local reaction-diffusion equation on bounded domain

Dynamical Behaviors of a Delayed Reaction-diffusion Equation

In this paper, we derive a delayed reaction-diffusion equation to describe a two-species predator-prey system with diffusion terms and stage structure. By coupling the uniformly approximate approach with the method of upper and lower solutions, we prove that the traveling wave fronts exist, which connect the zero solution with the positive steady state. Finally, we draw a conclusion that the ex...

Asymptotic Behavior of the Solutions of a Discrete Reaction-diffusion Equation

A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation

The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N²M) compared with O(NM) for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM) embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, ...

Uniform Permanence and Wavefronts for a Non-local Reaction-diffusion Equation with Delay∗

We consider scalar equation ut(t, x) = uxx(t, x)− u(t, x) + Z R K(x− y)g(u(t − h, y))dy, (∗) where g : R+ → R+ has exactly two fixed points: x1 = 0, x2 = κ > 0, and K is non-negative and such that R

A numerical investigation of a reaction-diffusion equation arises from an ecological phenomenon

This paper deals with the numerical solution of a class of reaction diffusion equations arises from ecological phenomena. When two species are introduced into unoccupied habitat, they can spread across the environment as two travelling waves with the wave of the faster reproducer moving ahead of the slower.The mathematical modelling of invasions of species in more complex settings that include ...