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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
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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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