Open Access Research

Uniform blow-up rate for a porous medium equation with a weighted localized source

Weili Zeng1, Xiaobo Lu2* and Qilin Liu3

Author affiliations

1 School of Transportation, Southeast University, Nanjing 210096, China

2 School of Automation, Southeast University, Nanjing 210096, China

3 Department of Mathematics, Southeast University, Nanjing 210096, China

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Citation and License

Boundary Value Problems 2011, 2011:57  doi:10.1186/1687-2770-2011-57

Published: 28 December 2011

Abstract

In this article, we investigate the Dirichlet problem for a porous medium equation with a more complicated source term. In some cases, we prove that the solutions have global blow-up and the rate of blow-up is uniform in all compact subsets of the domain. Moreover, in each case, the blow-up rate of |u(t)|is precisely determined.

Keywords:
porous medium equation; localized source; blow-up, uniform blow-up rate