Poincaré's inequality and diffusive evolution equations

Details Poincaré's inequality and diffusive evolution equations Poincaré's inequality and diffusive evolution equations

2007-11-10

arxiv.org/abs/0711.1626v1

Mathematics

Analysis of PDEs

16 pages. Submitted

Scientific paper

This paper addresses the question of change of decay rate from exponential to algebraic for diffusive evolution equations. We show how the behaviour of the spectrum of the Dirichlet Laplacian in the two cases yields the passage from exponential decay in bounded domains to algebraic decay or no decay at all in the case of unbounded domains. It is well known that such rates of decay exist: the purpose of this paper is to explain what makes the change in decay happen. We also discuss what kind of data is needed to obtain various decay rates.

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