Variational Characterization of the Speed of Propagation of Fronts for the Nonlinear Diffusion Equation

Abstract

We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equation $u_t=u_{xx}+f(u)$ with $f(0)=f(1)=0$, and $f>0$ in $(0,1)$, which permits, in principle, the calculation of the exact speed for arbitrary $f$.

References in corpus (3)

• Structural Stability and Renormalization Group for Propagating Fronts
• On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation
• New exact fronts for the nonlinear diffusion equation with quintic nonlinearities

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• On the speed of pulled fronts with a cutoff
• Pushed traveling fronts in monostable equations with monotone delayed reaction
• A Variational Principle for Eigenvalue Problems of Hamiltonian Systems
• Variational approach to a class of nonlinear oscillators with several limit cycles
• Speed selection and stability of wavefronts for delayed monostable reaction-diffusion equations
• Critical Sharp Front for Doubly Nonlinear Degenerate Diffusion Equations with Time Delay
• Existence and uniqueness of monotone wavefronts in a nonlocal resource-limited model
• Variational characterization of the speed of reaction diffusion fronts for gradient dependent diffusion
• Phase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems
• On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation
• Upper and lower bounds for the speed of fronts of the reaction diffusion equation with Stefan boundary conditions
• On pushed wavefronts of monostable equation with unimodal delayed reaction
• On the principal bifurcation branch of a third order nonlinear long-wave equation