Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The quenching behavior of a semilinear heat equation with a singular boundary outflux

Authors: Burhan Selcuk and Nuri Ozalp
Journal: Quart. Appl. Math. 72 (2014), 747-752
MSC (2000): Primary 35K55, 35K60, 35B35, 35Q60
DOI: https://doi.org/10.1090/S0033-569X-2014-01367-9
Published electronically: September 26, 2014
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Abstract: In this paper, we study the quenching behavior of the solution of a semilinear heat equation with a singular boundary outflux. We prove a finite-time quenching for the solution. Further, we show that quenching occurs on the boundary under certain conditions and we show that the time derivative blows up at a quenching point. Finally, we get a quenching rate and a lower bound for the quenching time.

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Additional Information

Burhan Selcuk
Affiliation: Department of Computer Engineering, Karabuk University, Balıklarkayası Mevkii, 78050, Turkey
Email: bselcuk@karabuk.edu.tr

Nuri Ozalp
Affiliation: Department of Mathematics, Ankara University, Besevler, 06100, Turkey
Email: nozalp@science.ankara.edu.tr

DOI: https://doi.org/10.1090/S0033-569X-2014-01367-9
Keywords: Semilinear heat equation, singular boundary outflux, quenching, quenching point, quenching time, maximum principles.
Received by editor(s): November 28, 2012
Received by editor(s) in revised form: April 23, 2013
Published electronically: September 26, 2014
Article copyright: © Copyright 2014 Brown University

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