The Fujita phenomenon in exterior domains under the Robin boundary conditions

Jean-François Rault (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

The Fujita phenomenon for nonlinear parabolic problems ∂tu = ∆u + up in an exterior domain of RN under the Robin boundary conditions is investigated in the superlinear case. As in the case of Dirichlet boundary conditions, it turns out that there exists a critical exponent p = 1+2/N such that blow-up of positive solutions always occurs for subcritical exponents, whereas in the supercritical case global existence can occur for small non-negative initial data.

Mots clés: Nonlinear parabolic problems; Robin boundary conditions; Global solutions; Blow-up.; Blow-up

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Rault. The Fujita phenomenon in exterior domains under the Robin boundary conditions. 2010. ⟨hal-00524161⟩