Regular solutions to initial-boundary value problems in a half-strip for two-dimensional Zakharov–Kuznetsov equation. (February 2020)

• Record Type: Journal Article
• Authors: Faminskii, Andrei V.
• Is Part Of: Nonlinear analysis. Volume 51(2020)
• Publication Date: 2020-02
• Subjects: Zakharov–Kuznetsov equation -- Initial–boundary value problem -- Global solution -- Regularity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.06.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Initial–boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov–Kuznetsov equation are considered. Results on global well-posedness in classes of regular solutions in the cases of periodic and Neumann boundary conditions, as well as on internal regularity of solutions for all types of boundary conditions are established. Also in the case of Dirichlet boundary conditions one result on long-time decay of regular solutions is obtained.