Mathematics Colloquium

Alexander Mielke

(Weierstraß-Institut Berlin)

"On a metric and geometric approach to reaction-diffusion systems as gradient systems"

Date: Mon, December 1, 2014
Time: 17:15
Place: Research II Lecture Hall

Abstract: We discuss reaction-diffusion systems with reactions satisfying mass-action kinetics and the detailed-balance condition. They allow for a gradient structure where the dual dissipation potential is the sum of a transport (or Kantorovich-Wasserstein) part for diffusion and a reaction part. Similar structures are developed for the temperature-dependent case when the internal energy is used as variable.

The dissipation potential plays formally the role of an infinite-dimensional Riemannian tensor, which induces a Riemannian distance, called dissipation distance in this context. In the pure diffusion case this gives the Kantorovich-Wasserstein distance. We show that in a simple case including a reaction the induced dissipation distance, called Hellinger-Kantorovich distance, can be characterized explicitly.

This is joint work with Matthias Liero (WIAS Berlin) and Giuseppe Savare (Pavia).

The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.