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