QUENCHING FOR A SEMILINEAR HEAT
EQUATION WITH A SINGULAR BOUNDARY OUTFLUX
Burhan Selcuk1, Nuri Ozalp2
1Department of Computer Engineering
Karabuk University, Balıklar Mevki
78050 Karabuk, TURKEY
2Department of Mathematics
Ankara University
06100 Ankara, TURKEY
Abstract. In this paper, we study the quenching behavior of solution of a semilinear heat equation with a singular boundary outflux. We first get a local existence result for this problem. We prove finite time quenching for the solution, we show that quenching occurs on the boundary and the time derivative blows up at the quenching time under certain conditions. Finally, we get a quenching rate and a lower bound for quenching time.
AMS Subject Classification: 35K20, 35K55, 35B50
Key Words and Phrases: semilinear heat equation, singular boundary outflux, quenching, maximum principles, monotone iterations


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DOI: 10.12732/ijam.v29i4.4

Volume: 29
Issue: 4
Year: 2016