Talk
On the applicability of Doeblin Harris type methods to PDE models with partial diffusion
Talk by Prof. Dr. Didier Smets
Speaker invited by: Prof. Dr. Klaus Widmayer
Date: 23.05.23 Time: 16.15 - 18.00 Room: ETH HG G 43
The Doeblin Harris method is a well established tool in the study of long time asymptotics for Markov processes. In recent years, it has gained popularity in the PDE community, while adapting to problems for which more traditional tools such as e.g. entropy methods did not seem directly applicable. In the talk we present a simple PDE model involving partial diffusion for which such a strategy turned up fruitful. Extensions to a wider class of models coming from neurosciences raise some interesting questions related to pointwise lower bounds for Green's functions in situations where Hörmander's iterated bracket condition is not satisfied, at least not everywhere. This is joint and ongoing work with Delphine Salort.