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Mathematical analysis of elastic surface waves in topographic waveguides. (English) Zbl 0946.74034
The authors study guided waves in an isotropic homogeneous elastic half-space with curvilinear surface. The problem is reduced to a family of two-dimensional eigenproblems in the cross-section of the wave-guide. Using the minimax principle for non-compact self-adjoint operators, the authors prove existence of guided waves for some particular geometries of the curvilinear surface. These waves have a finite transverse energy, and a velocity smaller than the velocity of Rayleigh waves in the half-space with plane surface.

MSC:
74J15 Surface waves in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
47N99 Miscellaneous applications of operator theory
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