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April  1997, 3(2): 175-188. doi: 10.3934/dcds.1997.3.175

Existence and blow up of small amplitude nonlinear waves with a negative potential

Walter A. Strauss 1, and  Kimitoshi Tsutaya 2,

1. 

Department of Mathematics and LCDS, Brown University, Providence, RI 02912, United States
2. 

Department of Mathematics, Brown University, Providence, R.I. 02912, United States

Received  November 1996 Published  January 1997

Consider a nonlinear wave equation in three space dimensions with zero mass together with a negative potential. If the potential is sufficiently short-range, then it does not alter the global existence of small-amplitude solutions. On the other hand, if the potential is sufficiently large, it will force some solutions to blow up in a finite time.
Keywords: Nonlinear wave equation, negative potential..
Mathematics Subject Classification: 35L70, 35B3.
Citation: Walter A. Strauss, Kimitoshi Tsutaya. Existence and blow up of small amplitude nonlinear waves with a negative potential. Discrete and Continuous Dynamical Systems, 1997, 3 (2) : 175-188. doi: 10.3934/dcds.1997.3.175
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