A variational principle for the kramers equation with unbounded external forces
Document Type
Article
Publication Date
10-1-2000
Identifier/URL
SCOPUS_ID:0034288692
Abstract
A time discrete variational principle is developed for the Cauchy problem of the Kramers equation with unbounded external force fields. The variational scheme is based on the idea of maximizing a relative entropy with respect to the Kantorovich functional associated with a certain cost function. Convergence of the scheme is established. Consequently, global existence of weak solutions of the Kramers equation with a broad class of unbounded force fields and initial data is obtained. Our results also show that, in some senses, the Kramers dynamics follows, at each instant of time, the direction of a steepest descent of a free energy functional with respect to the Kantorovich functional. © 2000 Academic Press.
Repository Citation
Huang, C.
(2000). A variational principle for the kramers equation with unbounded external forces. Journal of Mathematical Analysis and Applications, 250, 333-367.
https://corescholar.libraries.wright.edu/math/339
DOI
10.1006/jmaa.2000.7109
