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arXiv · 1001.2773

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

Graeme W. Milton·John R. Willis
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Abstract

Minimization variational principles for linear elastodynamic, acoustic, or electromagnetic time-harmonic waves in dissipative media were obtained by Milton, Seppecher and Bouchitté 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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Graeme W. Milton, John R. Willis. 2010-01-15. Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin--Shtrikman type. https://doi.org/10.1098/rspa.2010.0006

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