On the singular limit of a boundary delayed Kuramoto-Sivashinsky-Korteweg-de Vries equation: Well-posedness and stability results

This article is concerned with a Kuramoto–Sivashinsky-Korteweg-de Vries equation in bounded interval. The as well one of the boundary conditions are supposed to be subject presence parameter $ \nu> 0 $. Moreover, this specific condition has time-delay effect. As \nu tends zero, we show that can obtain findings [4,58] concerning two Korteweg–de equations. Indeed, able retrieve well-posedness and stability results for problem without delay [58] [4] under same conditions, singular limit Kuramoto–Sivashinsky delay. proof based well-known Galerkin method together multiplier technique.