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.