Tbilisi Mathematical Journal

Long-time behaviour for Hirota equation

Xianyun Guo and Chaosheng Zhu

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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

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

Received: 21 December 2011
Revised: 10 July 2012
Accepted: 13 September 2012
First available in Project Euclid: 12 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Hirota equation global attractor exponential attractor


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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