## 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
On Global Solutions and Blow-up Solutions of Nonlinear Kirchhoff Strings with Nonlinear Dissipation
β Scribed by Kosuke Ono
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 299 KB
- Volume
- 216
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
When b s 0, Eq. 1.1 becomes usual semilinear wave equations. When Ε½ . 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
π SIMILAR VOLUMES
## Abstract In this paper we investigate the global existence and finite time blowβup of solutions to the nonlinear viscoelastic equation associated with initial and Dirichlet boundary conditions. Here β__j__ denote the subβdifferential of __j__. Under suitable assumptions on __g__(Β·), __j__(Β·) an
We study on the initial-boundary value problem for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation: When the initial energy associated with the equations is non-negative and small, a unique (weak) solution exists globally in time and has some decay properties.