Reflection and transmission of mechanical waves are considered for a uniaxially-inhomogeneous viscoelastic layer, which is sandwiched between two homogeneous half-spaces. The problem is framed within the time domain as originated by a normally-incident wave. The outgoing character of the reflected and transmitted waves is represented by appropriate conditions at the boundary of the layer. Next uniqueness is established for an initial value problem through an energy functional. The proof is first given for isotropic solids and then is generalized to anisotropic solids.
He, S. , Ström, S. and Weston, V.H.Time Domain Wave-Splittings and Inverse Problems, Oxford University Press, Oxford , 1998.
2.
Morro, A.split fields and direction of propagation for the solution to first-order systems of equations . Mathematical and Computer Modelling, 35, 1377-1389 (2002).
3.
Caviglia, G. and Morro, A.Wave splitting for first-order systems of equations . International Journal of Mathematics and Mathematical Sciences, 32, 371-381 (2002).
4.
Caviglia, G. and Morro, A.Existence and uniqueness in the reflection-transmission problem . Quarterly Journal of Mechanics and Applied Mathematics, 52, 543-564 (1999).
5.
Colton, D. and Kress, R.Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Berlin , 1992.
6.
Bassanini, P.Wave reflection from a system of plane waves . Wave Motion, 8, 311-319 (1986).
7.
Cesari, L.A boundary value problem for quasilinear hyperbolic systems in the Schauder canonic form . Annali della Scuola Normale Superiore di Pisa. 1, 311-358 (1974).
8.
Caviglia, G. and Morro, A. Existence and uniqueness for wave propagation in inhomogeneous elastic solids. Rendiconti del Seminario Matematico dell’Università di Padova, 108, 53-66 (2002).
9.
Fabrizio, M. and Morro, A.Mathematical Problems in Linear Viscoelasticity, SIAM, Philadelphia, PA , 1992.
10.
Miklowitz, J.The Theory of Elastic Waves and Waveguides, North-Holland, Amsterdam , 1978.
11.
Hayes, M.Inhomogeneous plane waves . Archive for Rational Mechanics and Analysis, 85, 41-79 (1984).
12.
Caviglia, G. and Morro, A.Inhomogeneous Waves in Solids and Fluids, World Scientific, Singapore , 1992
13.
Boulanger, Ph. and Hayes, M.Bivectors and Waves in Mechanics and Optics, Chapman and Hall, London , 1993.
