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

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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

Abstract
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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 & Continuous Dynamical Systems - A, 1997, 3 (2) : 175-188. doi: 10.3934/dcds.1997.3.175

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