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Blow-up for the Porous Media Equation with Source Term and Positive Initial Energy

✍ Scribed by Enzo Vitillaro

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 190 KB
Volume: 247
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6847

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✦ Synopsis

We study the Cauchy᎐Dirichlet problem for the porous media equation with nonlinear source term in a bounded subset of ‫ޒ‬ n . The problem describes the propagation of thermal perturbations in a medium with a nonlinear heat-conduction coefficient and a heat source depending on the temperature. The aim of the paper is to extend the unstable set to a part of the positive energy region, a phenomenon which was known only for linear conduction.

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