Qualitative properties for solutions of semilinear heat equations with strong absorption ✩

We are concerned with nonnegative solutions to the Cauchy problem ut − Δu + b(x, t )|u|p−1u =0 inRN ×(0,∞), u(x, 0) = u0(x) in RN. Here 0 0, α 2, A>0). We investigate the dependence of such phenomena as comparison principle, instantaneous shrinking of the support and existence on the behaviour of b(x, t ).  2003 Elsevier Science (USA). All rights reserved.