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

Manh Hong Duong, Yulong Lu

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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
Pages (from-to)5707-5727
JournalDiscrete and Continuous Dynamical Systems - Series A
Volume39
Issue number10
DOIs
Publication statusPublished - 1 Oct 2019

Keywords

  • operator splitting
  • variational method
  • fractional kinetic Fokker-Planck equation
  • kinetic transport equation
  • optimal transportation

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