DAMPING OF KINETIC TRANSPORT EQUATION WITH DIFFUSE BOUNDARY CONDITION.

We 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 R³ with the smooth boundary of the diffuse boundary condition. We prove the theorem by establishing a novel L¹-L∞ framework via stochastic cycles. [ABSTRACT FROM AUTHOR]