Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin--Shtrikman type

Details Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin--Shtrikman type Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin--Shtrikman type

2010-01-15

arxiv.org/abs/1001.2773v1

Physics

Mathematical Physics

23 pages 0 figures

Scientific paper

Minimization variational principles for linear elastodynamic, acoustic, or electromagnetic time-harmonic waves in dissipative media were obtained by Milton, Seppecher and Bouchitt\'e generalizing the quasistatic variational principles of Cherkaev and Gibiansky. Here a further generalization is made to allow for a much wider variety of boundary conditions, and in particular Dirichlet and Neumann boundary conditions. In addition minimization or maximization principles of the Hashin-Shtrikman type, incorporating "polarization fields", are developed.

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