Speaker: Jiaxin Jin (The Ohio State University)
Title: Damping of kinetic transport equation with diffuse boundary condition
Abstract: We first prove that exponential moments of a fluctuation of the pure transport equation decay pointwisely almost as fast as $t^{-3}$ when the domain is any general strictly convex subset of $\R^3$ with the smooth boundary of the diffuse boundary condition. The key of the proof is to establish a novel $L^1$-$L^\infty$ framework via stochastic cycles. Next we consider the model in an upper half space $T^2 \times \R_{+}$ subjected to gravitation-dominant conservative force field. At the boundary, the molecules bounces back following the non-isothermal diffusive reflection boundary condition. Then we show the moments of a fluctuation of the pure transport equation has exponential decay.
Zoom: https://osu.zoom.us/j/93517408580?pwd=M1dlWXo1L3oyYXZhY2JFdHRiV0JGQT09
Meeting ID: 935 1740 8580 Password: 314159
