We investigate the asymptotic behavior of solutions to damped hyperbolic equations involving strongly degenerate differential operators. First we establish the existence of a global attractor for the damped hyperbolic equation under consideration. Then we prove the finite dimensionality of the global attractor.
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Original Russian Text Copyright © 2016 Luyen D.T. and Tri N.M.
Ninh Nhat; Hanoi. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 4, pp. 809–829, July–August, 2016; DOI: 10.17377/smzh.2016.57.407. Original article submitted March 20, 2015.
The authors are supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) (Grant 101.02–2014.50).
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Luyen, D.T., Tri, N.M. Large-time behavior of solutions to degenerate damped hyperbolic equations. Sib Math J 57, 632–649 (2016). https://doi.org/10.1134/S0037446616040078
- global solution
- global attractor
- Lyapunov functional
- degenerate damped hyperbolic equation
- finite dimensionality of attractors