Ergodicity of transition semigroups for stochastic fast diffusion equations

doi:10.1007/s11464-011-0112-2

Front Math Chin

2011, Vol. 6

Issue (3) : 449-472 https://doi.org/10.1007/s11464-011-0112-2

RESEARCH ARTICLE

Ergodicity of transition semigroups for stochastic fast diffusion equations

Wei LIU(

)

Fakult?t für Mathematik, Universit?t Bielefeld, D-33501 Bielefeld, Germany

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Abstract

In this paper, we first show the uniqueness of invariant measures for the stochastic fast diffusion equation, which follows from an obtained new decay estimate. Then we establish the Harnack inequality for the stochastic fast diffusion equation with nonlinear perturbation in the drift and derive the heat kernel estimate and ultrabounded property for the associated transition semigroup. Moreover, the exponential ergodicity and the existence of a spectral gap are also investigated.

Keywords Harnack inequality invariant measure ergodicity fast diffusion equation heat kernel spectral gap

Corresponding Author(s): LIU Wei,Email:wei.liu@uni-bielefeld.de

Issue Date: 01 June 2011

Cite this article:

Wei LIU. Ergodicity of transition semigroups for stochastic fast diffusion equations[J]. Front Math Chin, 2011, 6(3): 449-472.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-011-0112-2
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I3/449

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