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

Authors : Dorina RĂDUCANU

Pages : 615-621

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Publication Date : 2015-06-01

Article Type : Research Paper

Abstract :In this paper, we study the quenching behavior of solution of a nonlinear parabolic equation with a singular boundary condition. We prove finite-time quenching for the solution. Further, we show that quenching 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 : Analytic functions, integral operator, Loewner chain, univalence criterion