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A uniqueness theorem for the reduced wave equation governing the acoustic wave in a heterogeneous medium. (English) Zbl 0647.73002

A uniqueness theorem is established for the scattering of harmonic small amplitude longitudinal (acoustic) waves by a body with spatially varying material parameters, which are real analytic on \({\bar \Omega}_ j\), \(\Omega_ j\) the elements of the smallest finite cover \(\{\Omega_ j\}\) of a ‘scatterer’ \(D_ 1\subset {\mathbb{R}}^ 3\). The cover has a tree like structure ‘to handle any nested regions’. This structure gives the theorems relevance to computational solution of the reduced wave equation by finite element methods.
Reviewer: J.Dunwoody

MSC:

74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74J99 Waves in solid mechanics
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74E05 Inhomogeneity in solid mechanics
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