552 RWTH Publication No: 811908        2020       
TITLE Boundary Control of Vlasov--Fokker--Planck Equations
AUTHORS Michael Herty, Shi Jin, 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.