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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Blow-up for degenerate parabolic equations with nonlocal source
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by Youpeng Chen, Qilin Liu and Chunhong Xie PDF
Proc. Amer. Math. Soc. 132 (2004), 135-145 Request permission

Abstract:

This paper deals with the blow-up properties of the solution to the degenerate nonlinear reaction diffusion equation with nonlocal source $x^{q}u_{t}-(x^{\gamma }u_{x})_{x}=\int _{0}^{a}u^{p}dx$ in $(0,a)\times (0,T)$ subject to the homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally or blows up in finite time are obtained. Furthermore, it is proved that under certain conditions the blow-up set of the solution is the whole domain.
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Additional Information
  • Youpeng Chen
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • Address at time of publication: Department of Mathematics, Yancheng Teachers College, Yancheng 224002, Jiangsu, People’s Republic of China
  • Email: youpengchen@263.sina.net, youpchen@yahoo.com.cn
  • Qilin Liu
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • Chunhong Xie
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • Received by editor(s): August 20, 2002
  • Published electronically: May 9, 2003
  • Communicated by: David S. Tartakoff
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 135-145
  • MSC (2000): Primary 35K55, 35K57, 35K65
  • DOI: https://doi.org/10.1090/S0002-9939-03-07090-4
  • MathSciNet review: 2021256