Electron. J. Diff. Equ., Vol. 2015 (2015), No. 311, pp. 1-13.

### 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