Wall, David J. N. A uniqueness theorem for the reduced wave equation governing the acoustic wave in a heterogeneous medium. (English) Zbl 0647.73002 Q. J. Mech. Appl. Math. 41, No. 1, 141-153 (1988). 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 Keywords:scattering; harmonic small amplitude longitudinal (acoustic) waves; spatially varying material parameters; tree like structure; nested regions; finite element methods PDFBibTeX XMLCite \textit{D. J. N. Wall}, Q. J. Mech. Appl. Math. 41, No. 1, 141--153 (1988; Zbl 0647.73002) Full Text: DOI