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
DOI:
https://doi.org/10.1090/S0033-569X-2012-01278-5
Published electronically:
August 27, 2012
MathSciNet review:
3052089
Full-text PDF Free Access
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Additional Information
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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References
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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
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.