Initial trace of solutions of semilinear heat equation with absorption

Waad Al Sayed (1) , Laurent Veron (2)

1 College of Sciences and Humanities
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

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

Mots clés: initial trace; Heat equation; Singularities; Harnack inequalities; Radon measures; Borel measures; barrier; initial trace.

Domaines: Equations aux dérivées partielles [math.AP]

Waad Al Sayed, Laurent Veron. Initial trace of solutions of semilinear heat equation with absorption. 2013. ⟨hal-00800654v3⟩