Qualitative properties of solutions to semilinear heat equations with singular initial data

Abstract

This article concerns the nonnegative solutions to the Cauchy problem ut - ∆u + b(x, t) |u|p-1 u = 0 in ℝN x (0, ∞), u(x, 0) = u0(x) in ℝN. We investigate how the comparison principle, extinction in finite time, instantaneous shrinking of support, and existence of solutions depend on the behaviour of the coefficient b(x, t).