Global solutions for a 2D BENNEY-LIN type equation posed on rectangles and on a half-strip

TL;DR

This paper establishes the existence, uniqueness, and exponential decay of solutions for a 2D Benney-Lin type equation on rectangles and half-strips, advancing understanding of its mathematical properties.

Contribution

It provides the first rigorous analysis of solutions for the 2D Benney-Lin equation in these geometries, including decay rates.

Findings

Existence and uniqueness of regular solutions

Exponential decay rate of solutions

Analysis on rectangles and half-strips

Abstract

We formulate on rectangles and on the right horizontal half-strip initial-boundary value problems for a two-dimensional Benney-Lin type equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the norm of a regular solution have been established.