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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Manuscripta Mathematica.
( Vol. 69 NO.1 / (1990))
Global Smooth Solutions to a Class of Semilinear Wave Equations with Strong Nonlinearities
Hartmut Pecher,
Pages. 71-92
Abstract We consider the Cauchy problem for semilinear wave equations $u_{tt}-Delta u=g(u)$ in 3+1 dimensions with smooth but possibly large data. If $g$ is $C^{2,alpha}$ and bounded from above everywhere and from below for negative arguments the existence of a global classical solution is shown. If moreover $g$ is nonpositive and vanishes at least or order $2+epsilon$ at the origin and if the data decay sufficiently rapidly at infinity the scattering operator exists.
Contents 0. Introduction 1. Global Existence 2. Scattering Appendix
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