Quenching for a diffusive equation with a concentrated singularity

Abstract

The diffusion equation with a concentrated singular reaction $v_t=v_{xx} + \epsilon\delta(x-a)f(v)$ $(\epsilon>0, 0<a<1)$ is studied. Criteria for global existence and finite time quenching of the solution are established. The growth rate and estimate on quenching time are also given for a certain class of nonlinearities.