Dipartimento di Matematica ''F. Casorati''

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Entropy entropy-production estimates for energy-reaction diffusion systems

Prof. Alexander Mielke, WIAS, Berlino

Sala conferenze IMATI-CNR, Pavia - Tuesday, March 21, 2017 h.15:00

Abstract. 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.)

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Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
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