Hyperbolic versus parabolic asymptotics in kinetic theory toward fluid dynamic models

摘要

In this work we are interested in the hyperbolic limits in kinetic theory. We propose a nonstandard scaling to be understood as a sort of intermediate hyperbolic limit, which connects the (macroscopic) hyperbolic limiting behavior of the physical system with the microscopic properties usually obtained under parabolic scalings. We present our main result by means of a general kinetic frame for the intermediate hyperbolic limit which covers some well-known examples in kinetic theory (Vlasov-Poisson-Fokker-Planck systems and linear relaxation for Boltzmann-type equations in semiconductor theory, among others). We will also apply our methods to deal with the Kac approach to Boltzmann operators.