Abstract
We study the initial trace problem for positive solutions of semilinear heat equations with strong absorption. We show that in general this initial trace is an outer regular Borel measure. We emphasize in particular the case where u satisfies (E) ∂tu−Δu+tα|u|q−1u=0, with q>1 and α>−1 and prove that in the subcritical case 1<q<qα,N≔1+2(1+α)/N the initial trace establishes a one to one correspondence between the set of outer regular Borel measures in RN and the set of positive solutions of (E) in RN×R+.