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Journal Articles Mathematical Methods in the Applied Sciences Year : 2015

Fréchet differentiability of the elasto-acoustic scattered field with respect to Lipschitz domains

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Abstract

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 elas- tic 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.
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Dates and versions

hal-01195633 , version 1 (08-09-2015)

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Hélène Barucq, Rabia Djellouli, Elodie Estecahandy. Fréchet differentiability of the elasto-acoustic scattered field with respect to Lipschitz domains. Mathematical Methods in the Applied Sciences, 2015, pp.13. ⟨10.1002/mma.3444⟩. ⟨hal-01195633⟩
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