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March  2008, 1(1): 83-87. doi: 10.3934/dcdss.2008.1.83

Eventual local positivity for a biharmonic heat equation in RN

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, Germany

Received  September 2006 Revised  September 2007 Published  December 2007

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.
Keywords: eventual local positivity., biharmonic heat equation, instantaneous change of sign.
Mathematics Subject Classification: Primary: 35B50; Secondary: 35K3.
Citation: Filippo Gazzola, Hans-Christoph Grunau. Eventual local positivity for a biharmonic heat equation in RN. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 83-87. doi: 10.3934/dcdss.2008.1.83
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