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Optimal shape for elliptic problems with random perturbations

 

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Author: Buttazzo, Giuseppe
Maestre Caballero, Faustino
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2011-12
Published in: Discrete and Continuous Dynamical Systems. Series A, 31 (4), 1115-1128.
Document type: Article
Abstract: In this paper we analyze the relaxed form of a shape optimization problem with state equation − div a(x)Du = f in D boundary conditions on ∂D. The new fact is that the term f is only known up to a random perturbation ξ(x, ω). The goal is to find an optimal coefficient a(x), fulfilling the usual constraints α ≤ a ≤ β and Z D a(x) dx ≤ m, which minimizes a cost function of the form Z Ω Z D j x, ω, ua(x, ω) dxdP(ω). Some numerical examples are shown in the last section, to stress the difference with respect to the case with no perturbation.
Cite: Buttazzo, G. y Maestre Caballero, F. (2011). Optimal shape for elliptic problems with random perturbations. Discrete and Continuous Dynamical Systems. Series A, 31 (4), 1115-1128.
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URI: http://hdl.handle.net/11441/42113

DOI: http://dx.doi.org/10.3934/dcds.2011.31.1115

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