On the fundamental solution and a variational formulation for a degenerate diffusion of Kolmogorov type
File(s)
Accepted version
Author(s)
Duong, Manh Hong
Tran, Hoang Minh
Type
Journal Article
Abstract
In this paper, we construct the fundamental solution to a degenerate diffusion of Kolmogorov type and develop a time-discrete variational scheme for its adjoint equation. The so-called mean squared derivative cost function plays a crucial role occurring in both the fundamental solution and the variational scheme. The latter is implemented by minimizing a free energy functional with respect to the Kantorovich optimal transport cost functional associated with the mean squared derivative cost. We establish the convergence of the scheme to the solution of the adjoint equation generalizing previously known results for the Fokker-Planck
equation and the Kramers equation.
equation and the Kramers equation.
Date Issued
2018-07-01
Date Acceptance
2018-02-04
Citation
Discrete and Continuous Dynamical Systems - Series A, 2018, 38 (7), pp.3407-3438
ISSN
1078-0947
Publisher
American Institute of Mathematical Sciences
Start Page
3407
End Page
3438
Journal / Book Title
Discrete and Continuous Dynamical Systems - Series A
Volume
38
Issue
7
Copyright Statement
© 2018 American Institute of Mathematical Sciences
Subjects
0101 Pure Mathematics
0102 Applied Mathematics
Applied Mathematics
Publication Status
Published