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

Chen, Youpeng; Liu, Lihua

doi:10.1090/S0033-569X-2012-01278-5

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
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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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