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Open Access Research

Blow-up profile for a degenerate parabolic equation with a weighted localized term

Weili Zeng1*, Xiaobo Lu1, Shumin Fei1 and Miaochao Chen2

Author Affiliations

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

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

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Boundary Value Problems 2013, 2013:269  doi:10.1186/1687-2770-2013-269

Published: 12 December 2013

Abstract

In this paper, we investigate the Dirichlet problem for a degenerate parabolic equation <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/269/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/269/mathml/M1">View MathML</a>. We prove that under certain conditions the solutions have global blow-up, and the rate of blow-up is uniform in all compact subsets of the domain. Moreover, the blow-up profile is precisely determined.

Keywords:
degenerate parabolic equation; localized source; uniform blow-up rate