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MArch/April 2009 Poincaré's inequality and diffusive evolution equations
Clayton Bjorland, Maria E. Schonbek
Adv. Differential Equations 14(3/4): 241-260 (MArch/April 2009). DOI: 10.57262/ade/1355867266


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 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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Clayton Bjorland. Maria E. Schonbek. "Poincaré's inequality and diffusive evolution equations." Adv. Differential Equations 14 (3/4) 241 - 260, MArch/April 2009.


Published: MArch/April 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1169.35047
MathSciNet: MR2493562
Digital Object Identifier: 10.57262/ade/1355867266

Primary: 35Q35 , 76B03

Rights: Copyright © 2009 Khayyam Publishing, Inc.


Vol.14 • No. 3/4 • MArch/April 2009
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