On the asymptotics of solutions to the Neumann problem for hyperbolic systems in domains with conical points

Kokotov, A.; Plamenevskiĭ, B.

doi:10.1090/S1061-0022-05-00862-9

On the asymptotics of solutions to the Neumann problem for hyperbolic systems in domains with conical points
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by A. Kokotov and B. Plamenevskiĭ
Translated by: B. A. Plamenevskiĭ

St. Petersburg Math. J. 16 (2005), 477-506

DOI: https://doi.org/10.1090/S1061-0022-05-00862-9

Published electronically: May 2, 2005

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Abstract:

Hyperbolic systems of second-order differential equations are considered in a domain with conical points at the boundary; in particular, the equations of elastodynamics are discussed. The asymptotics of solutions near conical points is studied. The “hyperbolic character” of the asymptotics shows itself in the properties of the coefficients (stress intensity factors) depending on time. Some formulas for the coefficients are presented and sharp estimates in Soboloev’s norms are proved.

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