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Macroscopic limits and decay to equilibrium for kinetic equations with relaxation collision kernels and mass conservation

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If you have a question about this talk, please contact Mustapha Amrani .

Partial Differential Equations in Kinetic Theories

Recent 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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