[Back]

A. Vlasak:
"Shape Optimization for Non-linear Parabolic Problems on Surfaces";
Supervisor: L. Nannen, K. Sturm; Institut für Analysis und Scientific Computing, 2021; final examination: 2021-02-21.

Abstract
Shape optimization is concerned with finding optimal shapes in the sense that they minimize a cost functional, most often while satisfying one or more constraints. This work considers a
problem in the following context: The set of admissible shapes is the set of all closed, compact and smooth surfaces embedded in R3. The cost functional is the squared L2 norm of u − ud over the surface for a target function ud. The function u is given by the constraint and is the solution of a non-linear parabolic partial differential equation on the surface. While elliptic problems as well as problems on open domains are widely discussed, the studying of parabolic problems on
surfaces is a rather new field of research.