Control problems in the coefficients and the domain for linear elliptic equations
type: Item
instance of: scholarly article
title: Control problems in the coefficients and the domain for linear elliptic equations
author: Juan Casado-Díaz
author: Manuel Luna-Laynez
author: Faustino Maestre
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2024-10-16T00:00:00Z
review text: A mixture of two conductive materials, each limited in amount, with diffusion coefficients \(\alpha\) and \(\beta\) is placed in measurable subsets \(\omega^{\alpha}\) and \(\omega^{\beta}\) of \(\Omega\), respectively. The goal is to choose the sets \(\omega^{\alpha}\) and \(\omega^{\beta}\) such that the potential \(u\) in \(\omega^{\alpha} \cup \omega^{\beta}\), which solves a linear elliptic state equation with homogeneous boundary conditions, minimizes the functional \(\int_{\Omega} F(x,u)\,dx\).\N\NFor the formulated optimal design problem, optimality conditions are derived, and a numerical algorithm is presented along with some numerical simulations.
reviewed by: Wiesław Kotarski
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49M05
Mathematics Subject Classification ID: 49Q10
zbMATH DE Number: 7926979
zbMATH Keywords: optimal design
zbMATH Keywords: shape optimization
zbMATH Keywords: two-phase materials
zbMATH Keywords: relaxation
zbMATH Keywords: homogenization
zbMATH Keywords: discrete approximation
zbMATH Keywords: convergence
MaRDI profile type: Publication
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DOI: 10.1007/S13398-024-01662-4
description: scientific article; zbMATH DE number 7926979