We study the global existence, asymptotic behaviour, and global non-existence (blow-up) of solutions for the damped non-linear wave equation of Kirchho! type in the whole space: , and '0, with initial data u(x, 0)"u (x) and u R (x, 0)"u (x).
The Global Attractors for the Periodic Initial Value Problem For a Coupled Non-linear Wave Equation
✍ Scribed by Guo Boling; Yang Linge
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 451 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
The existence of global attractors of the periodic initial value problem for a coupled non-linear wave equation is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of uniform a priori estimates for time.
📜 SIMILAR VOLUMES
In the paper, we shall prove that almost everywhere convergent bounded sequence in a Banach function space X is weakly convergent if and only if X and its dual space X\* have the order continuous norms. It follows that almost everywhere convergent bounded sequence in ¸N #¸N (1(p , p (R) is weakly co