Project B06
(S)PDEs on time-dependent random domains

Project description

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. 

Principal Investigators

Ana Djurdjevac (University of Oxford)

Claudia Schillings (FU Berlin)

Project members

Max Orteu (FU Berlin)

Publications

• Djurdjevac, A., Kaarnioja, V., Orteu, M., & Schillings, C., 2026. Quasi-monte carlo for bayesian shape inversion governed by the poisson problem subject to gevrey regular domain deformations. In C. Lemieux & B. Feng (Hrsg.), Monte Carlo and Quasi-Monte Carlo 2024 (Bd. 522, S. 239–257). Springer Nature Switzerland. https://doi.org/10.1007/978-3-032-10590-5_10 

• Alphonse, A., Djurdjevac, A., Engström, E., & Hansen, E., 2026. Transmission problems and domain decompositions for non-autonomous parabolic equations on evolving domains. Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications. https://doi.org/10.4171/ifb/564 

• Bernardin, C., Djurdjevac, A., Gonçalves, P., & Schnee, L., 2026. Derivation of stochastic burgers on the line with a dirichlet boundary condition at the origin. Journal of Dynamics and Differential Equations. https://doi.org/10.1007/s10884-026-10498-y 

Preprints

• Djurdjevac, A., Kaarnioja, V., Orteu, M., Schillings, C., 2025. Quasi-Monte Carlo for Bayesian shape inversion governed by the Poisson problem subject to Gevrey regular domain deformations. https://doi.org/10.48550/ARXIV.2502.14661 

• Djurdjevac, A., Kaarnioja, V., Schillings, C., Zepernick, A.-A., 2025. Uncertainty quantification for stationary and time-dependent PDEs subject to Gevrey regular random domain deformations. https://doi.org/10.48550/ARXIV.2502.12345 

• Djurdjevac, A., Gerencsér, M., & Kremp, H., 2024. Higher order approximation of nonlinear SPDEs with additive space-time white noise. https://doi.org/10.48550/ARXIV.2406.03058 (A02, B06)