95-508 Benguria, R. D. and Depassier, M. C.
The Speed of Fronts of the Reaction Diffusion Equation. (12K, RevTex) Nov 30, 95
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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 $(0,1)$.

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