Article thumbnail

Boundary Control of Vlasov--Fokker--Planck Equations

By Michael Herty, Shi Jin and Yuhua Zhu

Abstract

We introduce a novel Lyapunov function for stabilization of linear Vlasov--Fokker--Planck type equations with stiff source term. Contrary to existing results relying on transport properties to obtain stabilization, we present results based on hypocoercivity analysis for the Fokker--Planck operator. The existing estimates are extended to derive suitable feedback boundary control to guarantee the exponential stabilization. Further, we study the associated macroscopic limit and derive conditions on the feedback boundary control such that in the formal limit no boundary layer exists

Topics: Mathematics - Optimization and Control
Year: 2020
OAI identifier: oai:arXiv.org:2002.04215

Suggested articles


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.