Tuesday, 21 March 2017, 3 p.m. (sharp),
Prof. Alexander Mielke, WIAS, Berlino
at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
ENTROPY ENTROPY-PRODUCTION ESTIMATES FOR ENERGY-REACTION DIFFUSION SYSTEMS
as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
We discuss how the recently developed energy-dissipation methods for reaction-diffusion systems can be generalized to the non-isothermal case. For this we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well estimates for the entropy production of the nonlinear reactions we give three methods to estimate the relative entropy by the total entropy production, namely (1) a constructive methods using higher norms, (2) a method using additional convexity assumption, and (3) a very general compactness methods. (This is joint work with Jan Haskovec, Sabine Hittmeir, Peter Markowich, and Markus Mittnenzweig.)