Some flows in shape optimization

Details Some flows in shape optimization Some flows in shape optimization

2010-02-12

arxiv.org/abs/1002.2501v1

Arch. Ration. Mech. Anal. 183, 1 (2007) 21-58

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00205-006-0002-z

Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of which is widely inspired by viscosity solutions. The main result is an inclusion preservation principle for generalized solutions. As a consequence, we obtain existence, uniqueness and stability of solutions. Asymptotic behavior for the flow is discussed: we prove that the solutions converge to a generalized Bernoulli exterior free boundary problem.

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