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Time harmonic wave propagation in one dimensional weakly randomly perturbed periodic media

Sonia Fliss 1 Laure Giovangigli 1 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this work we consider the solution of the time harmonic wave equation in a one dimensional periodic medium with weak random perturbations. More precisely, we study two types of weak perturbations: (1) the case of stationary, ergodic and oscillating coefficients, the typical size of the oscillations being small compared to the wavelength and (2) the case of rare random perturbations of the medium, where each period has a small probability to have its coefficients modified, independently of the other periods. Our goal is to derive an asymptotic approximation of the solution with respect to the small parameter. This can be used in order to construct absorbing boundary conditions for such media.
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Submitted on : Tuesday, March 10, 2020 - 4:45:48 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:05 PM
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  • HAL Id : hal-02504392, version 1


Sonia Fliss, Laure Giovangigli. Time harmonic wave propagation in one dimensional weakly randomly perturbed periodic media. SN Partial Differential Equations and Applications, In press, 1 (40). ⟨hal-02504392⟩



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