Calculus of Variations and Geometric Measure Theory

L. Giacomelli - S. Moll - F. Petitta

Optimal waiting time bounds for flux-saturated diffusion equations

created by giacomell on 05 Jul 2016
modified by giacomelli on 04 Feb 2021


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

ArXiv: 1607.01245v3 PDF


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