The quenching behavior of a nonlinear parabolic equation with a singular boundary condition

Year 2015, , 615 - 621, 01.06.2015

Nuri Ozalp , Burhan Selçuk

https://doi.org/10.15672/HJMS.2015449429

Abstract

In this paper, we study the quenching behavior of solution of a nonlin- ear parabolic equation with a singular boundary condition. We prove finite-time quenching for the solution. Further, we show that quench- ing occurs on the boundary under certain conditions. Furthermore, we show that the time derivative blows up at quenching point. Also, we get a lower solution and an upper bound for quenching time. Finally, we get a quenching rate and lower bounds for quenching time.

Keywords

Nonlinear parabolic equation, singular boundary condition, quench- ing, quenching point, quenching time, maximum principles

References

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