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Large-time behavior of solutions to degenerate damped hyperbolic equations

Siberian Mathematical Journal volume 57, pages 632–649 (2016)Cite this article

Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Hoa Lu University, Ninh Nhat, Vietnam

    D. T. Luyen

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    N. M. Tri

Authors
  1. D. T. Luyen
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  2. N. M. Tri
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Corresponding author

Correspondence to N. M. Tri.

Additional information

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

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  • DOI: https://doi.org/10.1134/S0037446616040078

Keywords

  • global solution
  • global attractor
  • Lyapunov functional
  • degenerate damped hyperbolic equation
  • l-trajectory
  • finite dimensionality of attractors