A set of travelling wave solutions to a hyperbolic generalization of the convectionreaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of the compactly supported soloutions, shock fronts, soliton-like solutions and peakons PACS codes: 02.30.Jr; 47.50.Cd; 83.10.Gr

to diffusion, a convection term is present. Our overall aim is to look at the effect of convection on the existence and What is the long-time effect of adding convention to a discretised reaction-diffusion equation? For linear problems, it is well known stability of the true and spurious fixed points. that convection may denormalise the process, and, in particular, The potential denormalising e...

We consider a model of stochastically interacting particles on 2~, where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate 7/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this ...

We study the large time behavior of positive solutions of the semilinear parabolic equation ut Uxx + e(g(u))x + f(u), 0 < x < L, e E R, subject to u(O,t) u(i,t) 0. The model problem in which the results apply is g(u) u and f(u) up 1 < m < p. The steady state problem is analyzed in some detail, and results about finite time blow up are proved.

The reaction-diffusion master equation (RDME) is commonly used to model processes where both the spatial and stochastic nature of chemical reactions need to be considered. We show that the RDME in many cases is inconsistent with a microscopic description of diffusion limited chemical reactions and that this will result in unphysical results. We describe how the inconsistency can be reconciled i...

We study the blow-up behavior for positive solutions of a reaction–diffusion equationwith nonnegative variable coefficient. When there is no stationary solution, we show that the solution blows up in finite time. Under certain conditions, we then show that any point with zero source cannot be a blow-up point. © 2012 Elsevier Ltd. All rights reserved.

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 ...

We study the nonlinear dynamics of a reaction-diffusion equation where the nonlinearity presents a discontinuity. We prove the upper semicontinuity of solutions and of the global attractor with respect to smooth approximations of the nonlinear term. We also give a complete description of the set of fixed points and study their stability. Finally, we analyze the existence of heteroclinic connect...