Vol. 4, No. 1, 2022
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Propagation of polarization in transmission problems

Sönke Hansen
Vol. 4 (2022), No. 1, 153–190
DOI: 10.2140/paa.2022.4.153
Abstract

For geometric systems of real principal type, we define a subprincipal symbol and derive a transport equation for polarizations which, in the scalar case, is a well-known equation of Duistermaat and Hörmander. We apply the transport equation to propagation of polarization in transmission problems of elastodynamics, to interior bulk waves as well as to free (Rayleigh) surface waves. Using spectral factorizations of matrix polynomials having real spectrum, we establish reflection and refraction laws of polarizations at the boundary and at interior interfaces. The results are not limited to isotropic elasticity.

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Keywords
subprincipal symbol, real principal type, linear elastodynamics
Mathematical Subject Classification
Primary: 35A27
Secondary: 74J05
Milestones
Received: 22 July 2021
Accepted: 24 November 2021
Published: 29 April 2022
Authors
Sönke Hansen
Institut für Mathematik
Universität Paderborn
Paderborn
Germany