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Global and blow-up solutions for a system of nonlinear hyperbolic equations with dissipative terms

✍ Scribed by Fuqin Sun; Mingxin Wang

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
224 KB
Volume
64
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we study a nonlinear hyperbolic system with strong damping. Firstly, by use of the successive approximation method and a series of classical estimates, we prove the local existence and uniqueness of weak solution. Secondly, via some inequalities, applying the potential method and the concave method, we discuss the asymptotic and blow-up behavior of weak solution with different conditions.

πŸ“œ SIMILAR VOLUMES

Global existence, blow up and asymptotic
Global existence, blow up and asymptotic behaviour of solutions for nonlinear Klein–Gordon equation with dissipative term
✍ Xu Runzhang πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 203 KB

## Abstract We study the Cauchy problem of nonlinear Klein–Gordon 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