1Department of Economic Mathematics, South Western University of Finance and Economics, Chengdu, 610074, China. E-mail: laishaoy@tom.com
2Department of Mathematics and Statistics Curtin University of Technology GPO box 1987 Perth Western Australia 6845. E-mail: yhwu@maths.curtin.edu.au
*Corresponding Author
†This project is supported by Australia Endeavour Cheung Kong Awards (ES05/29775).
In this paper, we consider an initial-boundary value problem for the following generalized Boussinesq water equation defined in a unit ball
The existence of mild solutions is established in the space where κ <5/2, and the solutions are constructed in the form of series of the small parameter present in the initial conditions. For −1/2 < κ < 5/2, the uniqueness is proved. In addition, the long-time asymptotics is obtained in explicit form.
Generalized Boussinesq water equation, initial-boundary value problem, long-time asymptotics
