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Online ISSN 1552-4485; Print ISSN 0033-569X
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
MathSciNet review:
3291826
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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