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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

The blow-up profile for a nonlocal nonlinear parabolic equation with a nonlocal boundary condition


Authors: Youpeng Chen and Lihua Liu
Journal: Quart. Appl. Math. 70 (2012), 759-772
MSC (2000): Primary 35A07, 35B40, 35K55, 35K57, 35K60
Published electronically: August 27, 2012
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Abstract: This paper deals with the blow-up properties of positive solutions to a nonlinear parabolic equation with a nonlocal reaction source and a nonlocal boundary condition. Under certain conditions, the blow-up criteria is established. Furthermore, under two additional conditions, the global blow-up behavior is shown, and when $ f(u)=u^{p}, 0<p\leq 1$, the blow-up rate estimates are also obtained.


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Additional Information

Youpeng Chen
Affiliation: School of Mathematics, Yancheng Normal University, Yancheng 224002, Jiangsu, People’s Republic of China
Email: youpengc@yahoo.com.cn

Lihua Liu
Affiliation: School of Mathematics, Yancheng Normal University, Yancheng 224002, Jiangsu, People’s Republic of China, and School of Science, Hehai University, Nanjing 210098, Jiangsu, People’s Republic of China
Email: liulihua11111@163.com

DOI: http://dx.doi.org/10.1090/S0033-569X-2012-01278-5
PII: S 0033-569X(2012)01278-5
Keywords: Nonlinear parabolic equation, nonlocal reaction source, nonlocal boundary condition, global blow-up, blow-up rate
Received by editor(s): February 17, 2011
Published electronically: August 27, 2012
Additional Notes: This research is supported by the research scheme of the natural science of the universities of Jiangsu province (08KJD110017)
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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