The Fujita phenomenon in exterior domains under the dynamical boundary conditions

Original · EN

The Fujita phenomenon for nonlinear parabolic problems ∂ tu = Δu + 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.