Initial trace of solutions of general semilinear heat equation

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 amphasize the particular case where $u$ solves $\prt u-\Delta u+t^\alpha u^q=0$, with $q>1$ and $\alpha>-1$.

Mots clés: Heat equation; Singularities; Radon measures; Borel measures; blow-up; barrier

Domaines: Equations aux dérivées partielles [math.AP]

Waad Al Sayed, Laurent Veron. Initial trace of solutions of general semilinear heat equation. 2013. ⟨hal-00800654v1⟩