The quenching phenomenon of a nonlocal semilinear heat equation with a weak singularity

This paper is concerned with the combined effects of nonlocal and weak nonlinearities upon the quenching behavior of the solution of a nonlocal semilinear heat equation. It is shown that under some conditions the solution will quench at some finite time. The point-wise quenching rate estimate is also given in a backward space–time parabola near the quenching point. Our result demonstrates that the nonlocal nonlinearity in fact affects the quenching rate to some extent. Finally we apply our results to analyze a nonlocal blow-up problem.