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The uniform existence of solutions for two-dimensional and three-dimensional semilinear wave equations with oscillatory data
Author(s):
Yin
Huicheng
Journal:
Proc. Amer. Math. Soc.
127
(1999),
195-198.
MSC (1991):
Primary 35L70
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:
- 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
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, China
Email:
Huicheng@nju.edu.cn
DOI:
10.1090/S0002-9939-99-04862-5
PII:
S 0002-9939(99)04862-5
Received by editor(s):
May 7, 1997
Communicated by:
Jeffrey B. Rauch
Copyright of article:
Copyright
1999,
American Mathematical Society
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