Talk by Eszter Sikolya

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).