𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Global attractors for 2-D wave equations with displacement-dependent damping

✍ Scribed by A. Kh. Khanmamedov

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
177 KB
Volume
33
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

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 ( )Γ—L 2 ( ) and H 2 ( )∩H 1 0 ( )Γ—H 1 0 ( ).

πŸ“œ SIMILAR VOLUMES

Global and exponential attractors for 3-
Global and exponential attractors for 3-D wave equations with displacement dependent damping
✍ Vittorino Pata; Sergey Zelik πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 155 KB

## Abstract A weakly damped wave equation in the three‐dimensional (3‐D) 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 finite‐dimensional global and exponential attract

Dimension of the Global Attractor for St
Dimension of the Global Attractor for Strongly Damped Nonlinear Wave Equation
✍ Shengfan Zhou πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 109 KB

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

Attractors for a damped wave equation on
Attractors for a damped wave equation on ℝ3 with linear memory
✍ Vittorino Pata πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 164 KB πŸ‘ 1 views

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

Well-posedness for the 2-D damped wave e
Well-posedness for the 2-D damped wave equations with exponential source terms
✍ Xiaosen Han; Mingxin Wang πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 213 KB

## Communicated by P. Sacks In this paper we study well-posedness of the damped nonlinear wave equation in XΓ—(0, ∞) with initial and Dirichlet boundary condition, where X is a bounded domain in R 2 ; x β‰₯ 0, xk 1 +l>0 with k 1 being the first eigenvalue of -D under zero boundary condition. Under t