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