## Abstract We study the Cauchy problem of nonlinear KleinโGordon 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
โฆ LIBER โฆ
Blow-up of solutions of strongly dissipative generalized Klein-Gordon equations
โ Scribed by Korpusov, Maxim O
- Book ID
- 120533434
- Publisher
- Turpion Limited
- Year
- 2013
- Tongue
- English
- Weight
- 379 KB
- Volume
- 77
- Category
- Article
- ISSN
- 1064-5632
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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