Finite dimensional exponential attractors for semilinear wave equations with damping
β Scribed by A Eden; A.J Milani; B Nicolaenko
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 536 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We consider the following doubly nonlinear parabolic equation in a bounded domain Ξ©ββ^3^: where the nonlinearity __f__ is allowed to have a degeneracy with respect to β~__t__~__u__ of the form β~__t__~__u__|β~__t__~__u__|^__p__^ at some points __x__βΞ©. Under some natural assumptions o
## Abstract A weakly damped wave equation in the threeβdimensional (3βD) space with a damping coefficient depending on the displacement is studied. This equation is shown to generate a dissipative semigroup in the energy phase space, which possesses finiteβdimensional global and exponential attract
The paper considers a particular type of closed-loop for the wave equation in one space dimension with damping acting at an arbitrary internal point, for which the uniform stabilization with exponential decay rate is shown. Applications to chains of coupled strings are also discussed.
## Communicated by M. A. Efendiev In this paper the long-time behaviour of the solutions of 2-D wave equation with a damping coefficient depending on the displacement is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H 1 0 ( )ΓL 2 ( ) and H 2 ( )
A damped semilinear hyperbolic equation on 1 with linear memory is considered in a history space setting. Viewing the past history of the displacement as a variable of the system, it is possible to express the solution in terms of a strongly continuous process of continuous operators on a suitable H