Global Journal of Pure and Applied Mathematics
Open Access
  • Year: 2005
  • Volume: 1
  • Issue: 2

Blow-up of Positive Solution of Quasilinear Parabolic Equations with Nonlinear Neumann Boundary Conditions1

  • Author:
  • Hailiang Zhang1,*, Zengrong Liu1, Wu Zhang2
  • Total Page Count: 9
  • Page Number: 225 to 233

1Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China.

2School of Computer Science and Engineering, Shanghai University, Shanghai 200072, People's Republic of China. E-mail: wzhang@mail.shu.edu.cn

*E-mail: hlzhang88wy@sxu.edu.cn

1This work is partially supported by the National Natural Science Foundation of China (10372054, 70431002); the Natural Science Foundation of Shanxi Province of China (20051004)”.

Abstract

This paper deals with the blow-up of positive solutions of the quasilinear parabolic equations subject to nonlinear Neumann boundary conditions . Under suitable assumptions on nonlinear functions a, f, b and initial data u0(x), the blow-up of the solutions in a finite time is proved by the maximum principles. The bounds of “blow-up time” and blow-up rate are obtained.

Keywords

Quasilinear parabolic equation, Nonlinear boundary condition, Blow-up, Maximum principle