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Solving PDEs in Domains with Complex Evolving Morphology - Rothschild Lecture

Offered By: Isaac Newton Institute for Mathematical Sciences via YouTube

Tags

Partial Differential Equations Courses Numerical Analysis Courses Differential Geometry Courses Finite Element Method Courses Computational Mathematics Courses Biophysics Courses Mathematical Biology Courses

Course Description

Overview

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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.

Syllabus

Date: Monday 14th September 2015 - 16:00 to


Taught by

Isaac Newton Institute for Mathematical Sciences

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