Regularity and Decay of Global Solutions for the Generalized Benney-Lin Equation Posed on Bounded Intervals and on a Half-Line

Initial-boundary value problems for the generalized Benney-Lin equation posed on bounded intervals and on the right half-line were considered. The existence and uniqueness of global regular solutions on arbitrary intervals as well as their exponential decay for small solutions and for a special choice of a bounded interval have been established.