RESEARCH ARTICLE

A degenerate parabolic system with localized sources and nonlocal boundary condition

  • Yongsheng MI , 1,2 ,
  • Chunlai MU 1
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  • 1. College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China
  • 2. College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling 408100, China

Received date: 06 Aug 2010

Accepted date: 09 Oct 2011

Published date: 01 Feb 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

This paper deals with the blow-up properties of the positive solutions to a degenerate parabolic system with localized sources and nonlocal boundary conditions. We investigate the influence of the reaction terms, the weight functions, local terms and localized source on the blow-up properties. We will show that the weight functions play the substantial roles in determining whether the solutions will blow-up or not, and obtain the blow-up conditions and its blow-up rate estimate.

Cite this article

Yongsheng MI , Chunlai MU . A degenerate parabolic system with localized sources and nonlocal boundary condition[J]. Frontiers of Mathematics in China, 2012 , 7(1) : 97 -116 . DOI: 10.1007/s11464-011-0163-4

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