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.

中文翻译：

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修正的Zakharov–Kuznetsov方程半带上的初边值问题

考虑了修改后的Zakharov-Kuznetsov方程具有不同边界条件的半带上的初边值问题。建立了关于温和和常规溶液类别的局部和全局适定性，温和溶液的内部规律性以及温和和常规溶液的长期衰减的结果。在无穷Sobolev空间中对解决方案进行加权。