![Sample our Physical Sciences journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/110819/TOC-Subject-Sample-2021-Physical-Sciences.jpg"})
Abstract
It is well known that the analysis of the large-time asymptotics of Fokker-Planck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here we highlight this connection from an applied PDE point of view.
In our unified presentation of the theory we present new results to the following topics: an elementary derivation of Bakry-Emery type conditions, results concerning perturbations of invariant measures with general admissible entropies, sharpness of convex Sobolev inequalities, applications to non-symmetric linear and certain non-linear Fokker-Planck type equations (Desai-Zwanzig model, drift-diffusion-Poisson model).
ACKNOWLEDGMENTS
This research was partially supported by the grants ERBFMRXCT970157 (TMR-Network) from the EU, the bilateral DAAD-Vigoni Program, the DFG under Grant-No. MA 1662/1-3, and the NSF (DMS-9500852). The first author acknowledges fruitful discussions with L. Gross and D. Stroock, the second author with D. Bakry, and the second and third authors interactions with C. Villani. Also we thank the anonymous referee for his extremely constructive comments.