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Some flows in shape optimization

Abstract : 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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Submitted on : Friday, February 12, 2010 - 10:09:10 AM
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Pierre Cardaliaguet, Olivier Ley. Some flows in shape optimization. Archive for Rational Mechanics and Analysis, Springer Verlag, 2007, 183 (1), pp.21-58. ⟨10.1007/s00205-006-0002-z⟩. ⟨hal-00456121⟩

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