Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation
โ Scribed by Qingyong Gao; Fushan Li; Yanguo Wang
- Book ID
- 111488672
- Publisher
- SP Versita
- Year
- 2010
- Tongue
- English
- Weight
- 328 KB
- Volume
- 9
- Category
- Article
- ISSN
- 1895-1074
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
When b s 0, Eq. 1.1 becomes usual semilinear wave equations. When ลฝ . b)0, we call Eq. 1.1 wave equations of Kirchhoff type which have been introduced in order to study the nonlinear vibrations of an elastic string by
The initial boundary value problem for non-linear wave equations of Kirchhoff type with dissipation in a bounded domain is considered. We prove the blow-up of solutions for the strong dissipative term u t and the linear dissipative term u t by the energy method and give some estimates for the life s
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