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

Walter A. Strauss; Kimitoshi Tsutaya

doi:10.3934/dcds.1997.3.175

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1997, Volume 3, Issue 2: 175-188. Doi: 10.3934/dcds.1997.3.175

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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
2.
Department of Mathematics, Brown University, Providence, R.I. 02912

Received: October 31, 1996

Published: March 1997

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Abstract

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, 35B35.

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