Search results for "associated exterior Dirichlet problem"

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Multi-parameter analysis of the obstacle scattering problem

2022

Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle 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 Δu + k 2 u = 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.

integral equationsshape sensitivity analysisassociated exterior Dirichlet problemDirichlet-to-Neumann operatorApplied MathematicsHelmholtz equation; acoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; shape sensitivity analysis; perturbed domain; integral equationsacoustic scatteringComputer Science ApplicationsTheoretical Computer Scienceperturbed domainMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaSignal ProcessingFOS: Mathematicsacoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; Helmholtz equation; integral equations; perturbed domain; shape sensitivity analysisHelmholtz equation35J25 35J05 35P25 31B10 45A05Mathematical PhysicsAnalysis of PDEs (math.AP)
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