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Fréchet differentiability of the elasto‐acoustic scattered field with respect to Lipschitz domains
Author(s) -
Barucq Helene,
Djellouli Rabia,
Estecahandy Elodie
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3444
Subject(s) - differentiable function , lipschitz continuity , boundary (topology) , domain (mathematical analysis) , mathematics , field (mathematics) , scattering , mathematical analysis , lipschitz domain , boundary value problem , pure mathematics , physics , optics
We analyse the dependence with respect to a given domain of the solution of a fluid‐structure interaction scattering problem. We establish that the scattered field is continuously Fréchet differentiable with respect to the shape of the elastic scatterer. Our proof assumes that the boundary of the scatterer as well as the admissible perturbations to be only Lipschitzian. Given the applied nature of this problem and its prevalence in engineering and numerical literature, this new result appears to be of practical interest. Copyright © 2015 John Wiley & Sons, Ltd.