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2002 On a class of parabolic equations with variable density and absorption
Robert Kersner, Guillermo Reyes, Alberto Tesei
Adv. Differential Equations 7(2): 155-176 (2002). DOI: 10.57262/ade/1356651849

Abstract

We investigate qualitative properties of solutions to the Cauchy problem for the equation $\rho(x)u_t=(u^m)_{xx}-c_0 u^p$, where $m>1$ and $c_0, p >0$; the initial data are nonnegative with compact support and the density $\rho(x)>0$ satisfies suitable decay conditions as $|x|\to\infty$. If $p \ge m$ and $\rho(x)$ decays not faster than $|x|^{-k}$, where $0 <k \le k^*:=2(p-1)/(p-m)$, the interfaces exist globally in time. On the contrary, if $\rho(x)$ decays faster than $|x|^{-k}$ with $k>k^*$, the interfaces can disappear in finite time. It is also proved that solutions go to zero uniformly as $t \to\infty $, at variance from the case $c_0=0$.

Citation

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Robert Kersner. Guillermo Reyes. Alberto Tesei. "On a class of parabolic equations with variable density and absorption." Adv. Differential Equations 7 (2) 155 - 176, 2002. https://doi.org/10.57262/ade/1356651849

Information

Published: 2002
First available in Project Euclid: 27 December 2012

zbMATH: 1223.35209
MathSciNet: MR1869559
Digital Object Identifier: 10.57262/ade/1356651849

Subjects:
Primary: 35K65
Secondary: 35B40 , 35K55

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.7 • No. 2 • 2002
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