On uniqueness of large solutions of nonlinear parabolic equations in nonsmooth domains

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

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We study the existence and uniqueness of the positive solutions of the problem (P): $\partial_tu-\Delta u+u^q=0$ ($q>1$) in $\Omega\times (0,\infty)$, $u=\infty$ on $\partial\Omega\times (0,\infty)$ and $u(.,0)\in L^1(\Omega)$, when $\Omega$ is a bounded domain in $\mathbb R^N$. We construct a maximal solution, prove that this maximal solution is a large solution whenever $q

Mots clés: Parabolic equations; singular solutions; self-similarity; removable singularities

Domaines: Equations aux dérivées partielles [math.AP]

Waad Al Sayed, Laurent Veron. On uniqueness of large solutions of nonlinear parabolic equations in nonsmooth domains. Advanced Nonlinear Studies, 2009, 9 (1), pp.149-164. ⟨hal-00300801v2⟩