On the Bernoulli free boundary problem and related shape optimization problems | Zendy

Mohammed Hayouni | Zendy; Antoine Henrot | Zendy; Nadia Samouh | Zendy

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On the Bernoulli free boundary problem and related shape optimization problems

Author(s) -

Mohammed Hayouni,

Antoine Henrot,

Nadia Samouh

Publication year - 2001

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/30

Subject(s) - bernoulli's principle , shape optimization , free boundary problem , boundary (topology) , mathematics , optimization problem , conformal map , convergence (economics) , boundary value problem , class (philosophy) , mathematical optimization , mathematical analysis , computer science , physics , finite element method , artificial intelligence , economics , thermodynamics , economic growth

This paper deals with the classical Bernoulli free boundary problem. We are interested in solving some shape optimization problems related to this free boundary problem. We prove the continuous dependence of the solution with respect to the data K , working with Hausdorff convergence. We can deduce an existence result for a large class of shape optimization problems. Finally, we give some ideas for a numerical method, based on the use of conformal mappings, to solve such problems in two dimensions.

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