We consider the acoustic field scattered by a bounded impenetrable obsta- cle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation ∆u + k2u = 0. We show that the solution u and its far field pattern u∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.
Dalla Riva M., Luzzini P., Molinarolo R., Musolino P. (2024). MULTI-PARAMETER PERTURBATIONS FOR THE SPACE-PERIODIC HEAT EQUATION. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 23(2), 144-164 [10.3934/cpaa.2024004].
MULTI-PARAMETER PERTURBATIONS FOR THE SPACE-PERIODIC HEAT EQUATION
Dalla Riva M.;
2024-01-01
Abstract
We consider the acoustic field scattered by a bounded impenetrable obsta- cle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation ∆u + k2u = 0. We show that the solution u and its far field pattern u∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.
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