# Talk by Eszter Sikolya

On March 19th, 2021, Prof. Dr. Eszter Sikolya (ELTE University, Budapest) gave a talk about "**Stochastic reaction-diffusion equations on networks**" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.

## Abstract

First, we consider diffusion equations on the edges of a finite, connected network with Kirchhoff-Robin type boundary conditions in the vertices. We show that the corresponding operator generates a semigroup on the $L^p$ space of the product of the edges and vertices for each $ 1\leq p\leq \infty$. Then we add reaction terms and Wiener type stochastic noise on the edges and in the vertices of the network. Using the results of van Neerven, Lunardi and Cerrai we can prove the existence and unicity of the mild solutions of the stochastic problem.

This is joint work with Mihály Kovács (Budapest, Göteborg).