Stabilization of regular solutions for the Zakharov-Kuznetsov equation posed on bounded rectangles and on a strip

TL;DR

This paper investigates the Zakharov-Kuznetsov equation on bounded domains, analyzing spectral properties and domain sizes, and proves exponential decay of regular solutions for these boundary value problems.

Contribution

It provides new spectral analysis and decay results for the Zakharov-Kuznetsov equation on bounded rectangles and strips, extending understanding of solution stabilization.

Findings

Spectral properties of the linearized operator are characterized.

Critical domain sizes for stability are identified.

Exponential decay of solutions is established.

Abstract

Initial-boundary value problems for the 2D Zakharov-Kuznetsov equation posed on bounded rectangles and on a strip are considered. Spectral properties of a linearized operator and critical sizes of domains are studied. Exponential decay of regular solutions for the original nonlinear problems is proved.