Nuri Ozalp, Burhan Selcuk
Abstract:
In this article, we study the blow up behavior of the heat equation
with
,
.
We also study the quenching behavior of the nonlinear parabolic equation
with
,
.
In the blow up problem, if
is a lower solution then we get the blow up occurs in a finite time at the
boundary
and using positive steady state we give criteria for blow up
and non-blow up. In the quenching problem, we show that the only quenching
point is
and
blows up at the quenching time, under certain
conditions and using positive steady state we give criteria for quenching
and non-quenching. These analysis is based on the equivalence between the
blow up and the quenching for these two equations.
Submitted May 27, 2015. Published July 20, 2015.
Math Subject Classifications: 35K20, 35K55, 35B50.
Key Words: Heat equation; nonlinear parabolic equation; blow up;
nonlinear boundary condition; quenching; maximum principle.
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Nuri Ozalp Department of Mathematics Ankara University Besevler, 06100, Turkey email: nozalp@science.ankara.edu.tr | |
Burhan Selcuk Department of Computer Engineering, Karabuk University Bali klarkayasi Mevkii, 78050, Turkey email: bselcuk@karabuk.edu.tr |
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