Nuri Ozalp, Burhan Selcuk
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
Besevler, 06100, Turkey
| Burhan Selcuk |
Department of Computer Engineering, Karabuk University
Bali klarkayasi Mevkii, 78050, Turkey
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