An operator splitting scheme for the fractional kinetic Fokker-Planck equation

Manh Hong Duong, Yulong Lu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper, we develop an operator splitting scheme for the fractional kinetic Fokker-Planck equation (FKFPE). The scheme consists of two phases: a fractional diffusion phase and a kinetic transport phase. The first phase is solved exactly using the convolution operator while the second one is solved approximately using a variational scheme that minimizes an energy functional with respect to a certain Kantorovich optimal transport cost functional. We prove the convergence of the scheme to a weak solution to FKFPE. As a by-product of our analysis, we also establish a variational formulation for a kinetic transport equation that is relevant in the second phase. Finally, we discuss some extensions of our analysis to more complex systems.

Original languageEnglish (US)
Pages (from-to)5707-5727
Number of pages21
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume39
Issue number10
DOIs
StatePublished - 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Fractional kinetic Fokker-Planck equation
  • Kinetic transport equation
  • Operator splitting
  • Optimal transportation
  • Variational method

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