Applied Mathematics seminar | Klemens Fellner, Entropy- and Duality Methods for Reaction-Diffusion Systems

The talk presents recent advances in the existence theory (weak and classical) and the large time-behaviour of systems of nonlinear reaction-diffusion equations.

We shall first present how a careful analysis of a suitable dual problem allows to deduce, for instance, for quadratic non-linear reversible reaction-diffusion systems, global weak and classical solutions depending on the space dimension.

Moreover, we shall apply the so called entropy-method in order to prove exponential convergence to equilibrium with explicitly computable rates. Here, the key estimate is an entropy entropy-dissipation estimate, which bounds the entropy dissipation functional below in terms of the relative entropy with respect to the equilibrium.