Design of a Composite Membrane with Patches

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-010-9098-5· OSTI ID:21480259

Cuccu, Fabrizio ^[1]; Emamizadeh, Behrouz ^[2]; Porru, Giovanni ^[1]

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1. University of Cagliari, Dipartimento di Matematica e Informatica (Italy)
2. Petroleum Institute, Department of Mathematics (United Arab Emirates)

This paper is concerned with minimization and maximization problems of eigenvalues. The principal eigenvalue of a differential operator is minimized or maximized over a set which is formed by intersecting a rearrangement class with an affine subspace of finite co-dimension. A solution represents an optimal design of a 2-dimensional composite membrane {Omega}, fixed at the boundary, built out of two different materials, where certain prescribed regions (patches) in {Omega} are occupied by both materials. We prove existence results, and present some features of optimal solutions. The special case of one patch is treated in detail.

• OSTI ID: 21480259
• Journal Information: Applied Mathematics and Optimization, Vol. 62, Issue 2; Other Information: DOI: 10.1007/s00245-010-9098-5; Copyright (c) 2010 Springer Science+Business Media, LLC; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
EIGENVALUES
MATHEMATICAL SOLUTIONS
MEMBRANES
MINIMIZATION
TWO-DIMENSIONAL CALCULATIONS
OPTIMIZATION