Optimal waiting time bounds for some flux-saturated diffusion equations

Abstract

We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence of a waiting time phenomenon. We also prove optimal upper bounds on the waiting time. Our argument is based on the introduction of suitable families of subsolutions and on a comparison result for a general class of flux-saturated diffusion equations.

Comm. Partial Differential Equations, to appear

References in corpus (2)

• Pattern formation in a flux limited reaction-diffusion of porous media type
• Analysis of a class of degenerate parabolic equations with saturation mechanisms

Cited by in corpus (1)

• Nonlinear diffusion in transparent media: the resolvent equation