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

Abstract

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 $f^{\prime }(0)=0$ is included as an extension of the results.

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References in corpus (1)

• On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation

Cited by in corpus (4)

• Minimal speed of fronts of reaction-convection-diffusion equations
• Variational Approach of Critical Sharp Front Speeds in Density-dependent Diffusion Model with Time Delay
• Critical Sharp Front for Doubly Nonlinear Degenerate Diffusion Equations with Time Delay
• Variational characterization of the speed of reaction diffusion fronts for gradient dependent diffusion