ON THE DEAD-CORE PROBLEM FOR THE $p$-LAPLACE EQUATION WITH A STRONG ABSORPTION

JONG-SHENQ GUO; CHIN-CHIN WU

doi:10.2748/tmj/1450798072

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

ON THE DEAD-CORE PROBLEM FOR THE $p$-LAPLACE EQUATION WITH A STRONG ABSORPTION

JONG-SHENQ GUO, CHIN-CHIN WU

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Keywords: Dead-core, $p$-Laplace equation, strong absorption, self-similar solution

JOURNAL FREE ACCESS

2015 Volume 67 Issue 4 Pages 541-551

DOI https://doi.org/10.2748/tmj/1450798072

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Abstract

We study an initial boundary value problem for the $p$-Laplace equation with a strong absorption. We are concerned with the dead-core behavior of the solution. First, some criteria for developing dead-core are given. Also, the temporal dead-core rate for certain initial data is determined. Then we prove uniqueness theorem for the backward self-similar solutions.

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