The Speed of Fronts of the Reaction Diffusion Equation

Abstract

We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t=u_{xx}+f(u)$\, with $f(0)=f(1)=0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to $u=0$. No assumptions are made on the reaction term $f(u)$ other than those needed to guarantee the existence of the front. Therefore our results apply to the classical case $f>0$ in $(0,1)$, to the bistable case and to cases in which $f$ has more than one internal zero in $(0,1)$.

7 pages Revtex, 1 figure not included

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