Browsing by Author "Muga, Ignacio"

Now showing 1 - 3 of 3
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    Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary
    (ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2009) Duran, Mario; Muga, Ignacio; Nedelec, Jean Claude
    In this Note we deduce an explicit Sommerfeld-type radiation condition which is convenient to prove the uniqueness for the time-harmonic outgoing wave problem in an isotropic elastic half-plane with free boundary condition. The expression is obtained from a rigorous asymptotic analysis of the associated Green's function. The main difficulty is that the free boundary condition allows the propagation of a Rayleigh wave which cannot be neglected in the far field expansion. We also give the existence result for this problem. To cite this article: M. Duran et al., C R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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    The Helmholtz equation in a locally perturbed half-plane with passive boundary
    (OXFORD UNIV PRESS, 2006) Duran, Mario; Muga, Ignacio; Nedelec, Jean Claude
    In this article, we study the existence and uniqueness of outgoing solutions for the Helmholtz equation in locally perturbed half-planes with passive boundary. We establish an explicit outgoing radiation condition which is somewhat different from the usual Sommerfeld's one due to the appearance of surface waves. We work with the help of Fourier analysis and a half-plane Green's function framework. This is an extended and detailed version of the previous article Duran et al.
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    THE OUTGOING TIME-HARMONIC ELASTIC WAVE IN A HALF-PLANE WITH FREE BOUNDARY
    (SIAM PUBLICATIONS, 2011) Duran, Mario; Muga, Ignacio; Nedelec, Jean Claude
    Under a time-harmonic assumption, we prove existence and uniqueness results for the outgoing elastic wave in an isotropic half-plane, where the source is given by a local normal stress excitation of the free boundary. This is the starting point for problems of elastic wave scattering by locally perturbed flat surfaces. The main difficulty is that the free boundary condition induces the propagation of a Rayleigh surface wave guided by the unbounded flat frontier. Due to the presence of this surface wave in the far field expansion, we need to impose a new radiation condition in order to describe both volume and surface outgoing wave behavior and to show uniqueness.