Stabilization for the linear Zakharov–Kuznetsov equation without critical size restrictions

Initial–boundary value problems for the linear 2D Zakharov–Kuznetsov equation posed on bounded rectangles and on a channel-like strip are considered. We suggest a condition on a part of the boundary such that the evolution problem posed on a bounded rectangle has no critical restrictions on its size. The similar results are obtained both for a 2D strip and a 3D groove with no limitations on their width and gauge. Exponential decay rates of solutions for the original problems are established.