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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

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


Authors: A. Kokotov and B. Plamenevskii
Translated by: B. A. Plamenevskii
Original publication: Algebra i Analiz, tom 16 (2004), nomer 3.
Journal: St. Petersburg Math. J. 16 (2005), 477-506
MSC (1991): Primary 35C20, 35L20
Published electronically: May 2, 2005
MathSciNet review: 2083566
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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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Additional Information

A. Kokotov
Affiliation: Concordia University, Montreal, Canada
Email: kokotov@online.ru

B. Plamenevskii
Affiliation: Department of Physics, St. Petersburg State University, Ulyanovskaya 1, Petrodvorets, St. Petersburg 198504, Russia
Email: boris.plamenevskij@pobox.spbu.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-05-00862-9
PII: S 1061-0022(05)00862-9
Keywords: Hyperbolic systems, weighted estimates, asymptotics
Received by editor(s): December 1, 2003
Published electronically: May 2, 2005
Article copyright: © Copyright 2005 American Mathematical Society