Burhan Selcuk, Nuri Ozalp
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
Bali klarkayasi Mevkii 78050, Turkey
email: firstname.lastname@example.org, email@example.com
| Nuri Ozalp |
Department of Mathematics, Ankara University
Besevler 06100, Turkey
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