OPTIMAL DESIGN OF LOW-CONTRAST TWO-PHASE STRUCTURES FOR THE WAVE EQUATION

摘要: This paper is concerned with the following optimal design problem: find distribution of two phases in a given domain that minimizes an objective function evaluated through solution wave equation. type optimization problem known to be ill-posed sense it generically does not admit minimizer among classical admissible designs. Its relaxation could found, principle, homogenization theory but, unfortunately, always explicit, particular for functions depending on gradient. To circumvent this difficulty, we make simplifying assumption have low constrast. Then, second-order asymptotic expansion respect small amplitude phase coefficients yields simplified which amenable by means H-measures. We prove general existence theorem larger class composite materials and propose numerical algorithm compute minimizers context. As case elliptic state equation, composites are shown rank-one laminates. However, proof small-amplitude limit commute more delicate than case.