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

摘要

We study travelling fronts of equations of the form $u_{tt} + \phi(u) u_x =u_{xx} + f(u)$. A criterion for the transition from linear to nonlinearmarginal stability is established for positive functions $\phi(u)$ and for anyreaction 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 reactiondiffusion systems with transport memory.