The Speed of Fronts of the Reaction Diffusion Equation

Details The Speed of Fronts of the Reaction Diffusion Equation The Speed of Fronts of the Reaction Diffusion Equation

1995-11-29

arxiv.org/abs/patt-sol/9511003v1

Phys. Rev. Lett., 77 (1996) 1171

Nonlinear Sciences

Pattern Formation and Solitons

7 pages Revtex, 1 figure not included

Scientific paper

10.1103/PhysRevLett.77.1171

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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