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Zeitschrift für Analysis und ihre Anwendungen


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Volume 33, Issue 4, 2014, pp. 429–439
DOI: 10.4171/ZAA/1520

Published online: 2014-10-15

Asymptotic Behavior of Solutions for the Time-Delayed Kuramoto-Sivashinsky Equation

Chaosheng Zhu[1]

(1) Southwest University, Chongqing, China

In this paper, we investigate the asymptotic behavior of the solutions for the Kuramoto-Sivashinsky equation with a time delay. We prove the global existence of solutions and energy decay. By using the Liapunov function method, we shall show that the solution is exponentially decay if the delay parameter $\tau$ is sufficiently small.

Keywords: Kuramoto-Sivashinsky equation, time-delay, exponential decay, Liapunov function

Zhu Chaosheng: Asymptotic Behavior of Solutions for the Time-Delayed Kuramoto-Sivashinsky Equation. Z. Anal. Anwend. 33 (2014), 429-439. doi: 10.4171/ZAA/1520