A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem
| Type of publication: | Article |
| Citation: | 2007-34 |
| Publication status: | Published |
| Journal: | Applied Mathematics Letters |
| Volume: | 22 |
| Number: | 7 |
| Year: | 2009 |
| Pages: | 1025--1028 |
| Note: | Preprint no. 2007-34 |
| ISSN: | 0893-9659 |
| URL: | http://www.karlin.mff.cuni.cz/... |
| DOI: | 10.1016/j.aml.2009.01.027 |
| Abstract: | We study a semilinear hyperbolic problem, written as a second-order evolution equation in an infinite-dimensional Hilbert space. Assuming existence of the global attractor, we estimate its fractal dimension explicitly in terms of the data. Despite its elementary character, our technique gives reasonable results. Notably, we require no additional regularity, although nonlinear damping is allowed. |
| Userfields: | fjournal={Applied Mathematics Letters. An International Journal of Rapid Publication}, coden={AMLEEL}, mrclass={35B41 (34D45 34G20 35L70 37L30)}, mrnumber={MR2522993}, |
| Keywords: | Dimension of attractor, fractal dimension, Method of ℓ-trajectories, Nonlinear hyperbolic problem, Squeezing property |
| Authors | |
| Added by: | [ADM] |
| Total mark: | 0 |
|
Attachments
|
|
|
Notes
|
|
|
|
|
|
Topics
|
|
|
|
