The existence and estimate of the upper bound of the Hausdorff dimension of the global attractor for the strongly damped nonlinear wave equation with the Dirichlet boundary condition are considered by introducing a new norm in the phase space. The gained Hausdorff dimension decreases as the damping
Remark on the regularity of the global attractor for the wave equation with nonlinear damping
β Scribed by A.Kh. Khanmamedov
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 491 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The long-time behavior of the wave equation with nonmonotone interior damping is considered. It is shown that the semigroup generated by this equation possesses a global attractor in H 1 0 (β¦ ) Γ L 2 (β¦ ).
We prove that if the displacement coefficient of the damping of the 3D wave equation is a positive constant on the interval (-l, l), for large enough l > 0, then this equation has a strong global attractor in H 1 0 (β¦) Γ L 2 (β¦). We also show that this attractor is a bounded subset of H 2 (β¦) β© H 1
This paper deals with the regularity of the global attractor for the Klein}Gordon}Schro K dinger equation. Using a decomposition method, we prove that the global attractor for the one-dimensional model consists of smooth functions provided the forcing terms are regular.