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.
Key words
GBBM equations /
Cauchy problem /
initial boundary value problem /
strong solution
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References
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