  Initial-boundary value problems on a half-strip with different types of
boundary conditions for the generalized Kawahara-Zakharov-Kuznetsov equation
with nonlinearity of higher order are considered. In particular, nonlinearity
can be quadratic and cubic. Results on global existence and uniqueness in
classes of weak and strong solutions and large-time decay of small solutions
are established. The solutions are considered in weighted at infinity Sobolev
spaces. The use of weighted spaces is crucial for the study. To this end new
interpolating inequalities in weighted anisotropic Sobolev spaces are
established. Both exponential and power weights are admissible.
