Eventual local positivity for a biharmonic heat equation in RN

Filippo Gazzola; Hans-Christoph Grunau

doi:10.3934/dcdss.2008.1.83

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2008, Volume 1, Issue 1: 83-87. Doi: 10.3934/dcdss.2008.1.83

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Eventual local positivity for a biharmonic heat equation in R^N

Filippo Gazzola^1, and
Hans-Christoph Grunau^2,

1.
Dipartimento di Matematica Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano
2.
Fakultät für Mathematik, Otto-von-Guericke-Universität, Postfach 4120, 39016 Magdeburg

Received: August 31, 2006

Revised: August 31, 2007

Published: February 2008

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Abstract

We study the positivity preserving property for the Cauchy problem for the linear fourth order heat equation. Although the complete positivity preserving property fails, we show that it holds eventually on compact sets.

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Mathematics Subject Classification: Primary: 35B50; Secondary: 35K30.

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Eventual local positivity for a biharmonic heat equation in R^N