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

Initial-Boundary Value Problems on a Half-Strip for the Generalized Kawahara-Zakharov-Kuznetsov Equation