Time decay for the nonlinear Klein-Gordon equation
Open Access
- 10 September 1968
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 306 (1486) , 291-296
- https://doi.org/10.1098/rspa.1968.0151
Abstract
It is shown that solutions of the nonlinear Klein-Gordon equation u tt - ∆ u + mu + P '( u ) = 0 decay to zero in the local L 2 mean if the initial energy is bounded provided s P ') s ) - 2 P ( s ) ≥ a P ( s ) ≥ 0 with a > 0. The local energy also decays. The proof is based on manipulating energy identities and requires that u have continuouś first derivatives and piecewise continuous second derivatives. The proof is also applicable to certain systems of equations.Keywords
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