An initial-boundary value problem in a strip for two-dimensional Zakharov-Kuznetsov-Burgers equation

TL;DR

This paper studies the initial-boundary value problem for a 2D Zakharov-Kuznetsov-Burgers equation in a strip, establishing global well-posedness and decay of solutions in Sobolev spaces.

Contribution

It provides the first rigorous analysis of well-posedness and decay properties for this specific 2D Zakharov-Kuznetsov-Burgers equation with boundary conditions.

Findings

Proved global well-posedness of solutions.

Established decay rates of solutions over time.

Analyzed solutions in Sobolev spaces.

Abstract

An initial-boundary value in a strip with homogeneous Dirichlet boundary conditions for two-dimensional Zakharov-Kuznetsov-Burgers equation is considered. Results on global well-posedness and long-time decay of solutions in Sobolev spaces are established.