Smoothing effect due to mixing in kinetic theorem and its application to the optical tomography

I-Kun Chen

Institute of Applied Mathematical Science

National Taiwan University

    In kinetic theorem, it is known that the combination of collision or averaging and transport can result gaining of regularity, e.g., the celebrated Velocity Averaging Lemma by Golse, Perthame, and Sentis 1985 and the Mixture Lemma by Liu and Yu 2004. For stationary solution in a bounded convex domain, we find this effect can be realized by interplaying between velocity and space. We can decompose the solution to functions of different level of regularity due to different times of mixing and use it for optical tomography.