Advances in Differential Equations

Poincaré's inequality and diffusive evolution equations

Clayton Bjorland and Maria E. Schonbek

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Abstract

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.

Article information

Source
Adv. Differential Equations Volume 14, Number 3/4 (2009), 241-260.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867266

Mathematical Reviews number (MathSciNet)
MR2493562

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 76B03: Existence, uniqueness, and regularity theory [See also 35Q35]

Citation

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.


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