The Fujita phenomenon in exterior domains under the dynamical boundary conditions

Abstract

The Fujita phenomenon for nonlinear parabolic problems $\partial tu=\Delta u+up$ in an exterior domain of RN under the dynamical 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.

13 pages