Linear and nonlinear marginal stability for fronts of hyperbolic reaction diffusion equations

Abstract

We study travelling fronts of equations of the form $u_{tt}+\varphi (u)u_x=u_{xx}+f(u)$. A criterion for the transition from linear to nonlinear marginal stability is established for positive functions $\varphi (u)$ and for any reaction term $f(u)$ for which the usual parabolic reaction diffusion equation $u_t=u_{xx}+f(u)$ admits a front. As an application, we treat reaction diffusion systems with transport memory.

5 pages + 1 figure, Revtex file

References in corpus (1)

• Effects of Transport Memory and Nonlinear Damping in a Generalized Fisher's Equation

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