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The uniform existence of solutions
for two-dimensional and three-dimensional
semilinear wave equations with oscillatory data


Author: Yin Huicheng
Journal: Proc. Amer. Math. Soc. 127 (1999), 195-198
MSC (1991): Primary 35L70
DOI: https://doi.org/10.1090/S0002-9939-99-04862-5
MathSciNet review: 1600098
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Abstract: For two-dimensional and three-dimensional semilinear wave equations, I prove the uniform existence of solutions with oscillatory initial data. Hence I solve an ``open question" in one paper of J. L. Joly, G. Metivier and J. Rauch.


References [Enhancements On Off] (What's this?)

  • 1. J. L. Joly, G. Metivier, J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics, Ann. Sci. Ecole Norm. Sup. 28 (1995), 51-113. MR 95k:35035
  • 2. L. Hormander, The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin-New York 2 (1983). MR 85g:35002b
  • 3. J. L. Joly, G. Metivier, J. Rauch, Nonlinear oscillations beyond caustics, Comm. Pure Appl. Math., Vol. XIIIX (1996), 443-527. MR 96m:35195
  • 4. J. L. Joly, G. Metivier, J. Rauch, Focusing at a point and absorption of nonlinear oscillations, Trans. Amer. Math. Soc. 347 (1995), 3921-3971. MR 95m:35024

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Additional Information

Yin Huicheng
Email: Huicheng@nju.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-99-04862-5
Received by editor(s): May 7, 1997
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1999 American Mathematical Society

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