On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation

Abstract

In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t=u_{xx}+f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the hamiltonian system $u_{xx}+f(u)=0$ and the asymptotic speed of propagation of fronts of the reaction diffusion equation. Based on this conjecture an explicit expression for the speed of the front is given. We give a counterexample to this conjecture and conclude that additional restrictions should be placed on the reaction terms for which it may hold.

9 pages Revtex plus 4 postcript figures

References in corpus (3)

• The Speed of Fronts of the Reaction Diffusion Equation
• Variational Characterization of the Speed of Propagation of Fronts for the Nonlinear Diffusion Equation
• On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation

Cited by in corpus (1)

• Front propagation into unstable states