Tbilisi Mathematical Journal

Long-time behaviour for Hirota equation

Abstract

In this paper, we investigate the long-time behavior of the solutions for the Hirota equation with the periodic boundary condition. At first, by time uniform priori estimates of solutions, we obtain the existence of global solutions. Furthermore, we prove the existence of a global attractor. Finally, by squeezing property and Lipschitz continuity, we prove the existence of an exponential attractor of finite fractal dimension which contains the global attractor.

Article information

Source
Tbilisi Math. J., Volume 5, Issue 1 (2012), 51-64.

Dates
Revised: 10 July 2012
Accepted: 13 September 2012
First available in Project Euclid: 12 June 2018

https://projecteuclid.org/euclid.tbilisi/1528768889

Mathematical Reviews number (MathSciNet)
MR3006758

Zentralblatt MATH identifier
1282.35065

Subjects
Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35B41: Attractors 35B45: A priori estimates

Citation

Guo, Xianyun; Zhu, Chaosheng. Long-time behaviour for Hirota equation. Tbilisi Math. J. 5 (2012), no. 1, 51--64. https://projecteuclid.org/euclid.tbilisi/1528768889

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