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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Smoothness of decaying wave motions
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by Jeffrey Rauch
Proc. Amer. Math. Soc. 49 (1975), 334-338
DOI: https://doi.org/10.1090/S0002-9939-1975-0367463-7
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Abstract:

We show that for compactly supported perturbations of the wave equation, solutions whose total energy decays to zero must be smooth, provided that there are no trapped rays.
References
  • Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
  • Lars Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations, Enseign. Math. (2) 17 (1971), 99–163. MR 331124
    • J. Rauch and M. Taylor, Decaying states of perturbed wave motion (to appear).
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 49 (1975), 334-338
  • MSC: Primary 35L15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0367463-7
  • MathSciNet review: 0367463