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Stabilization of Regular Solutions for the Zakharov-Kuznetsov Equation Posed on Bounded Rectangles and on a Strip

Published online by Cambridge University Press:  10 April 2015

G. G. Doronin  and
N. A. Larkin
G. G. Doronin
Affiliation:
Departamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, Paraná, Brazil (ggdoronin@uem.br; nlarkine@uem.br)
N. A. Larkin
Affiliation:
Departamento de Matemática, Universidade Estadual de Maringá, 87020-900 Maringá, Paraná, Brazil (ggdoronin@uem.br; nlarkine@uem.br)
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Abstract

Initial–boundary-value problems for the two-dimensional 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. An exponential decay rate of regular solutions for the original nonlinear problems is proved.

Keywords

ZK equationstabilizationexponential decaycritical domainsPrimary 35Q5335B35
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 3 , October 2015 , pp. 661 - 682
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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