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ISRN Mathematical Physics
Volume 2013 (2013), Article ID 673546, 8 pages
http://dx.doi.org/10.1155/2013/673546
Research Article

The Coupled Kuramoto-Sivashinsky-KdV Equations for Surface Wave in Multilayered Liquid Films

1Department of Mathematics, Weber State University, Ogden, UT 84408, USA
2Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA
3Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Received 4 June 2013; Accepted 5 July 2013

Academic Editors: S. C. Lim and W.-H. Steeb

Copyright © 2013 Maomao Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the coupled Kuramoto-Sivashinsky-KdV equations describing the surface waves on multilayered liquid films. A priori energy estimates for linearized problem are derived and local existence of solutions for initial-value problem is established.