Global solutions for the generalized Benney-Lin equation posed on bounded intervals and on a half-line

TL;DR

This paper establishes the existence, uniqueness, and exponential decay of global regular solutions for the generalized Benney-Lin equation on bounded intervals and half-line, advancing understanding of its boundary value problems.

Contribution

It provides new results on global solutions and their decay properties for the generalized Benney-Lin equation in various domain settings.

Findings

Existence and uniqueness of global regular solutions.

Exponential decay of small solutions.

Results applicable to bounded intervals and half-line.

Abstract

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.