Exponential attractors for the strongly damped wave equations
β Scribed by Meihua Yang; Chunyou Sun
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 553 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1468-1218
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π SIMILAR VOLUMES
we prove the existence of the global attractor for the semigroup generated by strongly damped wave equations when the nonlinearity has a critical growth exponent.
We consider the dynamical behavior of the strongly damped wave equations under homogeneous Neumann boundary condition. By the property of limit set of asymptotic autonomous differential equations, we prove that in certain parameter region, the system has a one-dimensional global attractor, which is
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
## 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