## New results for guided waves in heterogeneous elastic media.(English)Zbl 0756.35108

The paper investigates the propagation of guided waves in an isotropic (unbounded) elastic medium that is invariant under translation in one space direction and asymptotically homogeneous at infinity. The existence of guided waves propagating with a velocity strictly larger than the $$S$$ (shear) wave velocity at infinity is proved.
Following A. Bamberger, Y. Dermenjian and P. Joly [ Mathematical analysis of the propagation of elastic guided waves in heterogeneous media, INRIA Report No. 1013 (1989)], the existence of guided waves is formulated as an eigenvalues and eigenvectors problem for a family of self-adjoint (elastic) operators, and these waves correspond to the existence of eigenvalues embedded in the essential spectrum.
Reviewer: S.Jiang (Bonn)

### MSC:

 35Q72 Other PDE from mechanics (MSC2000) 35J50 Variational methods for elliptic systems 74J10 Bulk waves in solid mechanics 47A10 Spectrum, resolvent 74B20 Nonlinear elasticity

### Keywords:

existence of guided waves; existence of eigenvalues
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### References:

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