Macroscopic limits and decay to equilibrium for kinetic equations with relaxation collision kernels and mass conservation
Seminar Room 1, Newton Institute
AbstractRecent results on the rigorous derivation of nonlinear convection- diffusion equations (ranging from porous medium to fast diffusion models) from kinetic transport models will be reviewed. Entropy dissipation techniques are employed in combination with compensated compactness. Exponential convergence to global equilibria is derived by a general abstract strategy for proving hypocoercivity results. It relies on the construction of a Lyapunov functional by a modification of the quadratic relative entropy and is inspired by the theory of hypoellipticity.
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