Optimal waiting time bounds for some flux-saturated diffusion equations
Analysis of PDEs
2019-07-23 v3
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.
Cite
@article{arxiv.1607.01245,
title = {Optimal waiting time bounds for some flux-saturated diffusion equations},
author = {Lorenzo Giacomelli and Salvador Moll and Francesco Petitta},
journal= {arXiv preprint arXiv:1607.01245},
year = {2019}
}
Comments
Comm. Partial Differential Equations, to appear