Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 311, pp. 113.
Quenching behavior of semilinear heat equations with singular
boundary conditions
Burhan Selcuk, Nuri Ozalp
Abstract:
In this article, we study the quenching behavior of solution to the semilinear
heat equation
with
or
and
For this, we utilize the quenching problem
with
,
.
In the second problem, if
is an upper solution (a lower solution)
then we show that quenching occurs in a finite time, the
only quenching point is
(
) and
blows up at quenching
time. Further, we obtain a local solution by using positive steady
state. In the first problem, we first obtain a local solution by using
monotone iterations. Finally, for
(
), if
is an upper solution (a lower solution) then we show that quenching occurs
in a finite time, the only quenching point is
(
) and
blows
up at quenching time.
Submitted October 16, 2015. Published December 21, 2015.
Math Subject Classifications: 35K05, 35K15, 35B50.
Key Words: Heat equation; singular boundary condition; quenching;
maximum principle; monotone iteration.
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Burhan Selcuk
Department of Computer Engineering
Karabuk University
Bali klarkayasi Mevkii 78050, Turkey
email: bselcuk@karabuk.edu.tr, burhanselcuk44@gmail.com

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

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