This project aims to develop a theory for (stochastic) partial differential equations ((S)PDEs) on random time-dependent domains, and their numerical analysis. We will focus on regularity results for parabolic PDEs on these domains to enable quasi-Monte Carlo methods for numerical discretization, analyze well-posedness of SPDEs on time-dependent domains, and study SPDEs on less regular random time-dependent domains, such as those evolving with Brownian motion. The project will employ the domain mapping approach, mapping uncertain domains to a reference domain, and explore suitable settings for evolving spaces and mappings.
DFG Programme
CRC/Transregios
