Special Session 169: Inverse problems arising in partial differential equations and mathematical physics

Forward and inverse problems for the BGK model with in-flow boundary condition
Hanming Zhou
University of California Santa Barbara
USA
Co-Author(s):    Ru-Yu Lai, Hanming Zhou
Abstract:
In this talk, we will discuss the Bhatnagar-Gross-Krook (BGK) equation with in-flow boundary condition in a smooth bounded domain. First, we show that the BGK model linearized around a global Maxwellian admits a unique solution with some weighted $L^\infty$ bound if the initial data and boundary condition are small perturbation around the global Maxwellian. Second, we investigate unique reconstruction of the collision frequency of the BGK equation from the albedo operator, which maps from the in-flow density to the out-flow density. We utilize the linearization technique and highly concentrated in-flow density to infer the velocity-independent collision frequency. The talk is based on joint work with Ru-Yu Lai.