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arXiv · 1607.01245

Optimal waiting time bounds for some flux-saturated diffusion equations

Lorenzo Giacomelli·Salvador Moll·Francesco Petitta
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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.

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Lorenzo Giacomelli, Salvador Moll, Francesco Petitta. 2016-07-05. Optimal waiting time bounds for some flux-saturated diffusion equations. https://doi.org/10.1080/03605302.2017.1294179

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