Advances in Dynamical Systems and Applications
  • Year: 2007
  • Volume: 2
  • Issue: 2

On similarity solutions for a class of nonlinear diffusion equations with convection1

  • Author:
  • Martin Bohner1,, Meihong Guan2, Liancun Zheng2,
  • Total Page Count: 10
  • Page Number: 167 to 176

1University of Missouri-Rolla, Department of Economics and Finance, Rolla, MO 65401, USA.

2University of Science and Technology, Beijing, Department of Mathematics and Mechanics, Beijing 100083, China.

*E-mail: bohner@umr.edu

**E-mail: liancunzheng@sina.com

AMS subject classification: 34B15, 34B16, 35A05, 35A22.

Abstract

This paper deals with a class of nonlinear N-diffusion equations with convection. The unique self-similar solution of a free boundary problem is constructed utilizing the unique solution of a related singular nonlinear two-point boundary value problem. To obtain the main result, shooting methods and certain integral representations of solutions are used.

Keywords

Free boundary problem, similarity solution, two-point boundary value problem, shooting method, N-diffusion