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2012 Long-time behaviour for Hirota equation
Xianyun Guo, Chaosheng Zhu
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Tbilisi Math. J. 5(1): 51-64 (2012). DOI: 10.32513/tbilisi/1528768889

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.

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Xianyun Guo. Chaosheng Zhu. "Long-time behaviour for Hirota equation." Tbilisi Math. J. 5 (1) 51 - 64, 2012. https://doi.org/10.32513/tbilisi/1528768889

Information

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

zbMATH: 1282.35065
MathSciNet: MR3006758
Digital Object Identifier: 10.32513/tbilisi/1528768889

Subjects:
Primary: 35B40
Secondary: 35B41, 35B45

Rights: Copyright © 2012 Tbilisi Centre for Mathematical Sciences

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Vol.5 • No. 1 • 2012
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