Solving PDEs in Domains with Complex Evolving Morphology - Rothschild Lecture
Explore a comprehensive lecture on solving partial differential equations (PDEs) in domains with complex evolving morphology. Delve into the mathematical challenges associated with formulating PDEs in time-dependent domains, both in flat and curved space. Examine the theory of well-posedness for abstract parabolic PDEs on evolving Hilbert spaces using generalized Bochner spaces. Learn about the material derivative and weak material derivative concepts in evolving spaces. Investigate applications to various scenarios, including surface heat equations, bulk domain equations, coupled bulk-surface systems, and equations with dynamic boundary conditions. Discover the relevance of these concepts to cell biology applications and the development of evolving surface finite element spaces. Gain insights into using geometric PDEs for computing high-quality meshes and explore computational examples from cell biology that couple surface evolution with surface processes.