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Talagrand's T_2-Transportation inequality and Log-Sobolev inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

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Chinese Annals of Mathematics,Series B 2006年第3期27卷 243-262页

作者： Liming WU Zhengliang ZHANG Laboratoire de Mathématiques Appliquées CNRS-UMR 6620 Université Blaise Pascal 63177 Aubière France School of Mathematics and Statistics Wuhan University Wuhan 430072 China. School of Mathematics and Statistics Wuhan University Wuhan 430072 China.

We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction- Diffusion equations are provided.

关键词： Stochastic partial differential equations (SPDEs) Logarithmic Sobolev inequality Talagrand's transportation inequality poincaré inequality

NONLINEAR STABILITY FOR EADY'S MODEL

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Applied Mathematics and Mechanics(English Edition) 2005年第2期26卷 200-203页

作者：刘永明邱令存 Department of Mathematics East China Normal University Shanghai 200062 P.R.China

poincaré type integral inequality plays an important role in the study of nonlinear stability (in the sense of (Arnold's) second theorem) for three-dimensional quasi-geostophic flow. The nonlinear stability of (Eady's) model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite. To fill this gap, the enhanced poincaré inequality was obtained by considering the additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for (Eady's) model in the periodic channel, the linear stable implies the nonlinear stable.

关键词： poincaré inequality (Eady's) model nonlinear stability

poincaré Inequalities for Bounded Jump Processes

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Journal of Southwest Jiaotong University(English Edition) 2009年第2期17卷 174-176页

作者：陈文英 College of Mathematics and Computer Science Chongqing Three Gorges University

A lot of forms and applications have been found in poincar6 inequality, but the optimum constants satisfying poincar6 inequality have not been estimated. This paper estimates the optimum constants λ0 and λ1 satisfyi... 详细信息

关键词： Non-trivial probability space poincaré inequality Isoperimetric constants Bounded jump processes