A coupled system of Korteweg-de Vries equations as singular limit of the Kuramoto-Sivashinsky equations. (English) Zbl 1148.35078

The authors study a coupled system of generalized Kuramoto-Sivashinsky equations on a bounded interval. The equations and the boudnary conditions depend on an additional parameter \(\nu\) such that in the limit \(\nu \to 0\) the system reduces to a coupled system of the Korteweg-de Vries equations. The existence and uniqueness theorems for strong solutions of these systems are proved by using the Faedo-Galerkin method.


35Q53 KdV equations (Korteweg-de Vries equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)