Initial-boundary value problems on a half-strip for the modified Zakharov–Kuznetsov equation

Abstract

Initial-boundary value problems on a half-strip with different types of boundary conditions for the modified Zakharov–Kuznetsov equation are considered. Results on local and global well-posedness in classes of mild and regular solutions, internal regularity of mild solutions and long-time decay of both mild and regular solutions are established. The solutions are considered in weighted at infinity Sobolev spaces.