Advances in Differential Equations

Poincaré's inequality and diffusive evolution equations

Clayton Bjorland and Maria E. Schonbek

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Bjorland, Clayton; Schonbek, Maria E. Poincaré's inequality and diffusive evolution equations. Adv. Differential Equations 14 (2009), no. 3/4, 241--260.

Export citation