A coupled system of Korteweg-de Vries equations as singular limit of the Kuramoto-Sivashinsky equations (Q944178)

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.