Differential and Integral Equations

Quenching behavior for the solution of a nonlocal semilinear heat equation

Jong-Shenq Guo

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Abstract

We study the solution for the initial boundary value problem of a nonlocal semilinear heat equation. It is well-known that the solution quenches in finite time for certain choices of initial data. We first prove that there is only one quenching point for symmetric initial data with one peak. Then we derive a quenching rate estimate. It turns out that the constant in the quenching rate estimate depends on the solution itself due to the nonlocal nonlinearity.

Article information

Source
Differential Integral Equations Volume 13, Number 7-9 (2000), 1139-1148.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061214

Mathematical Reviews number (MathSciNet)
MR1775250

Zentralblatt MATH identifier
0984.35012

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 35K55: Nonlinear parabolic equations

Citation

Guo, Jong-Shenq. Quenching behavior for the solution of a nonlocal semilinear heat equation. Differential Integral Equations 13 (2000), no. 7-9, 1139--1148. https://projecteuclid.org/euclid.die/1356061214.


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