Quenching problem of a reaction-diffusion equation with time delay

The quenching problem for a parabolic equation with time delay where the spatial domain is a sphere in Rn is presented. The reaction-diffusion equation consists of D and τ as positive constants representing the diffusion coefficient and time delay, respectively, and f(u) as a reaction function which is singular at some point c*>0. It is assumed that f(u) is a C1-function in [0,c*) and the initial function η(t,r) is a nonnegative Holder continuous function in [-τ,0]×(0,R) and satisfies the boundary condition at t = 0.