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May/June 2011 Quenching rate of solutions for a semilinear parabolic equation
Masaki Hoshino
Adv. Differential Equations 16(5/6): 401-434 (May/June 2011).


We study the behavior of solutions of the Cauchy problem for a semilinear parabolic equation with a singular absorption term. We discuss the convergence of solutions to a singular stationary solution from above as time goes to infinity, and show that in a supercritical case a sharp estimate of the quenching rate can be determined explicitly when a specific growth rate of initial data is given. We also obtain a universal lower bound of the quenching rate which implies the optimality of the results. Proofs are given by a comparison method that is based on matched asymptotic expansion. We first determine a quenching rate of solutions by a formal analysis. Based on the formal analysis, we give a rigorous proof by constructing appropriate super- and subsolutions with the desired quenching rate.


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Masaki Hoshino. "Quenching rate of solutions for a semilinear parabolic equation." Adv. Differential Equations 16 (5/6) 401 - 434, May/June 2011.


Published: May/June 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1227.35168
MathSciNet: MR2816111

Primary: 35B35, 35B40, 35K15

Rights: Copyright © 2011 Khayyam Publishing, Inc.


Vol.16 • No. 5/6 • May/June 2011
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