Convergence of Global and Bounded Solutions of the Wave Equation with Linear Dissipation and Analytic Nonlinearity
β Scribed by Mohamed Ali Jendoubi
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 217 KB
- Volume
- 144
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
A functional analysis method is used to prove the existence and the uniqueness of solutions of a class of linear and nonlinear functional equations in the Hilbert Ε½ . Ε½ . space H β¬ and the Banach space H β¬ . In the case of the nonlinear functional 2 1 equation, a bound of the solution is also given.
We give an example of the influence of the dependence of the coefficient of equation on time variable, and in particular oscillations in time, on a global existence of the solution to the nonlinear hyperbolic equation. Namely for arbitrary small initial data we construct a blowing up solution.
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
## Abstract In this paper we prove the existence of global decaying __H__^2^ solutions to the Cauchy problem for a wave equation with a nonlinear dissipative term by constructing a stable set in __H__^1^(β^__n__^ ). (Β© 2008 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
## 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