The existence of steady solutions of the Kuramoto-Sivashinsky equation
نویسندگان
چکیده
منابع مشابه
Exact Solutions of the Generalized Kuramoto-Sivashinsky Equation
In this paper we obtain exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems. The methods used to determine the exact solutions of the underlying equation are the Lie group analysis and the simplest equation method. The solutions obtained are then plotted.
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Recent work on the dynamics of a crystal surface [T. Frisch and A. Verga, Phys. Rev. Lett. 96, 166104 (2006)] has focused the attention on the conserved KuramotoSivashinsky (CKS) equation: ∂tu = −∂xx(u+ uxx + ux), which displays coarsening. For a quantitative and qualitative understanding of the dynamics, the analysis of steady states is particularly relevant. In this paper we provide a detaile...
متن کاملexact solutions of the generalized kuramoto-sivashinsky equation
in this paper we obtain exact solutions of the generalized kuramoto-sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems. the methods used to determine the exact solutions of the underlying equation are the lie group analysis and the simplest equation method. the solutions obtained are then plotted.
متن کاملMeromorphic traveling wave solutions of the Kuramoto–Sivashinsky equation
We determine all cases when there exists a meromorphic solution of the ODE νw + bw + μw + w/2 +A = 0. This equation describes traveling waves solutions of the KuramotoSivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable t...
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Motivated by the work of Foias and Temam [C. Foias, R. Temam, Gevrey class regularity for the solutions of the Navier–Stokes equations, J. Funct. Anal. 87 (1989) 359–369], we prove the existence and Gevrey regularity of local solutions to the Kuramoto–Sivashinsky equation in Rn with initial data in the space of distributions. The control on the Gevrey norm provides an explicit estimate of the a...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1989
ISSN: 0022-0396
DOI: 10.1016/0022-0396(89)90134-4