On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis. (Q2712989)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis. |
scientific article |
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6 May 2001
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Fokker-Planck equation
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trend to equilibrium
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generalized porous medium equations
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sticky particle system
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logarithmic Sobolev inequalities
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Poincaré inequality
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On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis. (English)
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The paper presents connections between the problem of trend to equilibrium for the Fokker-Planck equation and the several inequalities from functional analysis. These inequalities are formulated in terms of relative entropy of probability measures and relative Fisher information. Such inequalities like logarithmic Sobolev or Poincaré inequalities as well as the inequalities arising in the context of concentration of measures or in the study of Gaussian isoperimetry are applied to the problems under consideration.NEWLINENEWLINEVarious examples illustrates the general statements. Among them are generalized porous medium equations, Monge-Ampère and Hamilton-Jacobi equations, the sticky particle system.
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