Published Paper
Inserted: 5 jul 2016
Last Updated: 4 feb 2021
Journal: Comm. Partial Differential Equations
Volume: 42
Number: 4
Pages: 556-578
Year: 2017
Doi: 10.1080/03605302.2017.1294179
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.
Keywords: conservation laws, entropy solutions, Waiting time phenomena , flux-saturated diffusion equations