zbMATH — the first resource for mathematics

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 \(\max (1,d/2)<p<\infty\).

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
Full Text: DOI
[1] Korteweg D. J., On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves 39 pp 422– (1895)
[2] Miura, R. M. 1976.The Korteweg-deVries equation: a survey of results, 412–459. SIAM Review. · Zbl 0333.35021
[3] Liu, B. P. and Pao, C.V. 1983.Green’s function method for periodic traveling wave solutions of the KdV equation, 292–301. Applicable Analysis. · Zbl 0515.35077
[4] Soewono, E. 1987.A remark on a paper by Liu and Pao on the, existence of periodic traveling wave solution to the KdV equation, 293–299. Applicable Analysis. · Zbl 0609.35079
[5] Liu, B. P. and Pao, C.V. 194.On periodic traveling wave solutions of Boussinesq equation, Quarterly of Applied Mathematics311–319. · Zbl 0598.76019
[6] Chen, Y. and Wen, S. 1987.Traveling wave solutions to the two-dimensional Korteweg-deVries equation, 226–236. J. of Math. Anal, and Appl. · Zbl 0634.35066
[7] Stakgold I., Green’s Functions and Boundary Value Problems75 (1979) · Zbl 0421.34027
[8] Wang I., Mathematics Handbook5 People’s Education (1977)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.