## Differential and Integral Equations

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

### Quenching behavior for the solution of a nonlocal semilinear heat equation

#### 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