International Journal of Applied Mathematical Sciences
  • Year: 2006
  • Volume: 3
  • Issue: 2

An Initial-Boundary Value Problem for a Generalized Boussinesq Water System in a Ball†

  • Author:
  • Shaoyong Lai1, Ying Wang1, Yong Hong Wu2,, Qun Lin2
  • Total Page Count: 17
  • Page Number: 117 to 133

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).

Abstract

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.

Keywords

Generalized Boussinesq water equation, initial-boundary value problem, long-time asymptotics