Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions
β Scribed by Tohru Ozawa; Kimitoshi Tsutaya; Yoshio Tsutsumi
- Book ID
- 110596533
- Publisher
- Springer-Verlag
- Year
- 1996
- Tongue
- French
- Weight
- 748 KB
- Volume
- 222
- Category
- Article
- ISSN
- 0025-5874
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π SIMILAR VOLUMES
This paper studies the Cauchy problem for the coupled system of nonlinear Klein-Gordon equations with damping terms. We first state the existence of standing wave with ground state, based on which we prove a sharp criteria for global existence and blow-up of solutions when E(0) < d. We then introduc
## Abstract We study the Cauchy problem of nonlinear KleinβGordon equation with dissipative term. By introducing a family of potential wells, we derive the invariant sets and prove the global existence, finite time blow up as well as the asymptotic behaviour of solutions. In particular, we show a s