An optimal design problem for a two-phase isolating material in the wall of a cavity. (November 2020)

• Record Type: Journal Article
• Authors: Casado-Díaz, Juan; Maestre, Faustino
• Is Part Of: Nonlinear analysis. Volume 200(2020)
• Publication Date: 2020-11
• Subjects: 49J20 -- 35B25 -- 35B40; Optimal design -- Two-phase material -- Isolating material -- Thin wall -- First eigenvalue; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.112025
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We are interested in the optimal distribution of two isolating materials in the wall of a cavity in order to get the best isolation when the amount of the best isolating material is limited. We assume that the wall is of width ε > 0 small. The problem can be formulated as the minimization of the first eigenvalue of a certain diffusion operator where the diffusion constant is of order one inside the cavity and of order ε in the wall. As it is usual in optimal design, the problem has not solution in general and therefore, it is necessary to work with a relaxed formulation. Passing to the limit when ε tends to zero we get an asymptotic model where the variable control is now in a Robin boundary condition instead of the diffusion operator. We also present some numerical simulations showing the behavior of the solutions.