Initial-boundary value problems in a rectangle for two-dimensional Zakharov–Kuznetsov equation

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov–Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution are established. As applications of the developed technique results on boundary controllability and long-time decay of weak solutions are also obtained. © 2018 Elsevier Inc.