A reaction-diffusion equation as a Hellinger-Kantorovich gradient flow
speaker: Alexander Mielke (WIAS Berlin and Humboldt University Berlin)abstract: Large classes of reaction-diffusion systems with reactions satisfying mass- action kinetics and the detailed-balance condition can be written as a formal gradient system with respect to the relative entropy. The the dual dissipation potential is the sum of a transport part for diffusion and a reaction part. We discuss the mathematical steps needed to turn the formal theory into a rigorous metric gradient system. Motivated by scalar reaction-diffusion equations we construct the so-called Hellinger- Kantorovich distance on the set of all non-negative measures. This distance can be obtained (i) via transport and growth, (ii) by the inf-convolution of the Kantorovich- Wasserstein distance and the Hellinger distance, and (iii) by minimizing a logarithmic- entropy transport problem. We provide examples of entropies and such that induced reaction-diffusion equation is a lambda-convex gradient flow. This is joint work with Matthias Liero (WIAS Berlin) and Giuseppe Savare (Pavia)
timetable:
Thu 30 Oct, 9:00 - 9:50, Aula Dini
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