The Fujita phenomenon in exterior domains under dynamical boundary conditions

The Fujita phenomenon for nonlinear parabolic problems partial derivative(t)u = Delta u + u(p) in an exterior domain of R(N) under dissipative dynamical boundary conditions sigma partial derivative(t)u + partial derivative(v)u = 0 is investigated in the superlinear case. As in the case of Dirichlet boundary conditions (see Trans. Amer. Math. Soc. 316 (1989), 595-622 and Israel J. Math. 98 (1997), 141-156), 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.