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Remark on the global existence for the generalized Benjamin-Bona-Mahony equations in arbitrary dimension. (English) Zbl 0631.35080
The global existence of the solutions to the initial boundary value problems of GBBM equations in arbitrary dimension d is further studied. It is proved that when the nonlinear function satisfies some polynomial- like growth bounds, there exists a unique global solution in the space C([0,\(\infty)\); \(W^{2,p}\cap W_ 0^{1,p})\), with \(\max (1,d/2)<p<\infty\).

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
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