高阶非齐次GBBM方程

ON INHOMOGENEOUS GBBM EQUATIONS OF HIGHER ORDER

本文研究了高阶非齐次ＧＢＢＭ方程的Ｃａｕｃｈｙ问题和初边值问题。对任意的有界或无界光滑区域Ω，采用Ｂａｎａｃｈ不动点原理及一系列的积分估计，建立了高阶非齐次ＧＢＢＭ方程的Ｃａｕｃｈｙ问题和初边值问题在Ｗ２ｍ，ｐ（Ω）上整体强解的存在唯一性，这些结果改进并完善了ＢＢＭ方程的已有结果，与此同时，我们还讨论了强解的正则性。

This paper concerns the Cauchy problem and the initial boundary value (IBV)problem for the inhomogeneous GBBM equations of higher order. For any bounded or unbounded smooth domain, the existence and uniqueness of global strong solution for the Cauchy problem and IBV problem of inhomogenous GBBM equations of higher order in W2m,p(Ω) are established by using Banach fixed point theorem and a prior estimates, these results (and results in it's Remarks) have improved the well known results even in the case of GBBM equation. Meanwhiles, we also discuss the regularity of the strong solution.