A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation

Details A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation

1994-10-27

arxiv.org/abs/patt-sol/9410001v1

Phys. Rev. E, 52 (1995) 3285

Nonlinear Sciences

Pattern Formation and Solitons

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Scientific paper

10.1103/PhysRevE.52.3285

We show that the minimal speed for the existence of monotonic fronts of the
equation $u_t = (u^m)_{xx} + f(u)$ with $f(0) = f(1) = 0$, $m >1$ and $f>0$ in
$(0,1)$ derives from a variational principle. The variational principle allows
to calculate, in principle, the exact speed for arbitrary $f$. The case $m=1$
when $f'(0)=0$ is included as an extension of the results.

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