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On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. (English) Zbl 0982.35113
The connection between the entropy approach for the analysis of the large-time asymptotics of Fokker-Planck type equations and convex Sobolev inequalities is highlighted. This unified presentation of the theory allows to obtain the following new results in various fields: an elementary derivation of Bakry-Emery type conditions, perturbations of invariant measures with general admissible entropies, sharpness of convex Sobolev inequalities, applications to non-symmetric linear and nonlinear Fokker-Planck type equations (Desai-Zwanzig model, drift-diffusion-Poisson model).

MSC:
35Q72 Other PDE from mechanics (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
82D37 Statistical mechanics of semiconductors
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
26D10 Inequalities involving derivatives and differential and integral operators
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