Existence and non-existence of solitary waves for the critical Klein–Gordon equation coupled with Maxwell's equations
✍ Scribed by Daniele Cassani
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 263 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0362-546X
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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
## Abstract In this paper we are concerned with the existence and energy decay of solution to the initial boundary value problem for the coupled Klein–Gordon–Schrödinger equations with non‐linear boundary damping and memory term. Copyright © 2006 John Wiley & Sons, Ltd.
E,H obeys Maxwell's equations 1.4 , 1.5 , and 1.6 . The unknown Ž . w . functions , , E, H depend on t, x g 0, ϱ , where t, x denote the time 1 2 and space variable resp. ⍀ ; ޒ 3 is a bounded Lipschitz-domain with Ѩ ⍀ s ⌫ j ⌫ , where ⌫ , ⌫ are disjoint subsets of Ѩ ⍀. ⌫ represents the D N D N D pe