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

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

1996-06-24

arxiv.org/abs/patt-sol/9606004v1

Phys. Rev. E., 55 (1997) 3701

Nonlinear Sciences

Pattern Formation and Solitons

9 pages Revtex plus 4 postcript figures

Scientific paper

10.1103/PhysRevE.55.3701

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.

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