Soft and Hard Wall in a Stochastic Reaction Diffusion Equation

Soft and Hard Wall in a Stochastic Reaction Diffusion Equation

We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two stable phases, as the intensity of the noise vanishes and the size of the interval diverges. In particular, we prove that, in a suitable scaling limit, the front ...

A stochastic pitchfork bifurcation in a reaction-diffusion equation

First we prove, for m 65, a lower bound on the dimension of the random attractor, which is of the same order in ­ as the upper bound we derived in an earlier paper, and is the same as that obtained in the deterministic case. Then we show, for m = 1, that as ­ passes through ¶ 1 (the ­ rst eigenvalue of the negative Laplacian) from below, the system undergoes a stochastic bifurcation of pitchfor...

Diffusion Equation and Stochastic Processes.

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 ...

A convergent reaction-diffusion master equation.

The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME is often interpreted as an approximation to spatially continuous models in which molecules move by Brownian motion and react by one of several mechanisms when sufficiently close. In the limit that the lattice spacing approa...