๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the existence of a global attractor for the wave equation with nonlinear strong damping perturbed by nonmonotone term

โœ Scribed by A.Kh. Khanmamedov

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
335 KB
Volume
69
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 (โ„ฆ ) ร— L 2 (โ„ฆ ).

๐Ÿ“œ SIMILAR VOLUMES

A strong global attractor for the 3D wav
A strong global attractor for the 3D wave equation with displacement dependent damping
โœ A.Kh. Khanmamedov ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 294 KB

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 (โ„ฆ) ร— L 2 (โ„ฆ). We also show that this attractor is a bounded subset of H 2 (โ„ฆ) โˆฉ H 1

Existence of a Solution of the Wave Equa
Existence of a Solution of the Wave Equation with Nonlinear Damping and Source Terms
โœ V. Georgiev; G. Todorova ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 375 KB

We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la