CMX Lunch Seminar

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 perturbations around the global Maxwellian. Second, we investigate the 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 (Minnesota).