Initial trace of solutions of semilinear heat equation with absorption

Waad Al Sayed, Laurent Veron

Published 2013-03-14, updated 2013-04-08Version 3

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) $\partial_t u-\Delta u+t^\alpha |u|^{q-1}u=0$, with $q>1$ and $\alpha>-1$ and prove that in the subcritical case $1