PoincarĂ©’s inequality and diffusive evolution equations. (English) Zbl 1169.35047

This paper addresses the question of change of decay rate from exponential to algebraic for diffusive evolution equations. The authors 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.


35Q35 PDEs in connection with fluid mechanics
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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