Existence and uniqueness for wave propagation in inhomogeneous elastic solids
type: Item
instance of: scholarly article
title: Existence and uniqueness for wave propagation in inhomogeneous elastic solids
zbMATH Open document ID: 1051.74023
author: Giacomo Caviglia
author: Angelo Morro
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2004-09-07T00:00:00Z
full work available at URL: https://eudml.org/doc/108593
review text: The problem of wave reflection and transmission in a layer sandwiched between two half-spaces is not a standard initial-boundary value problem because we do not known a priori a surface where the solution is known. For this problem, in one spatial dimension and when the inhomogeneity is taken into account, the authors are able to prove uniqueness of regular solutions by energy method, and to investigate the existence using Fourier analysis. The key idea is to write the boundary conditions in a way which directly accounts for the unknown waves propagating away from the scatterer, and to require the finiteness of the speed of propagation. In the particular homogeneous case this method provides also an exact solution of the problem in closed form. The authors note an analogy of this problem with some existence and uniqueness problems investigated by \textit{P. Bassanini} in electromagnetism and seismology [Wave Motion 8, 311--319 (1986; Zbl 0585.73178); Atti Semin. Mat. Fis. Univ. Modena 35, 335--356 (1987; Zbl 0673.35071)]. We point out that very important studies on the subject have been done by \textit{C. S. Morawetz} and coworkers [Proc. R. Ir. Acad., Sect. A 72, 113--120 (1972; Zbl 0239.35057); Comput. Math. Appl. 7, 319--331 (1981; Zbl 0465.35083); Math. Comput. 52, No. 186, 321-338 (1989; Zbl 0692.65068)].
reviewed by: Giuseppe Saccomandi
Mathematics Subject Classification ID: 74J05
Mathematics Subject Classification ID: 74H20
Mathematics Subject Classification ID: 74H25
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74E05
zbMATH DE Number: 2099238
zbMATH Keywords: energy method
zbMATH Keywords: Fourier analysis
MaRDI profile type: Publication
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cites work: Riccati equations for wave propagation in planarly-stratified solids
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cites work: Q3910929
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description: scientific article; zbMATH DE number 2099238