Advances in Differential Equations
- Adv. Differential Equations
- Volume 14, Number 3/4 (2009), 241-260.
Poincaré's inequality and diffusive evolution equations
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.
Adv. Differential Equations Volume 14, Number 3/4 (2009), 241-260.
First available in Project Euclid: 18 December 2012
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Bjorland, Clayton; Schonbek, Maria E. Poincaré's inequality and diffusive evolution equations. Adv. Differential Equations 14 (2009), no. 3/4, 241--260. https://projecteuclid.org/euclid.ade/1355867266