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Proceedings of the American Mathematical Society

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

 

 

Smoothness of decaying wave motions


Author: Jeffrey Rauch
Journal: Proc. Amer. Math. Soc. 49 (1975), 334-338
MSC: Primary 35L15
MathSciNet review: 0367463
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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 [Enhancements On Off] (What's this?)

  • [1] Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
  • [2] Lars Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations, Enseignement Math. (2) 17 (1971), 99–163. MR 0331124
  • [3] J. Rauch and M. Taylor, Decaying states of perturbed wave motion (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0367463-7
Article copyright: © Copyright 1975 American Mathematical Society