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The Fujita phenomenon for nonlinear parabolic problems dtu = \deltau + up inan exterior domain of RN under the Robin boundary conditions is investigated inthe superlinear case. As in the case of Dirichlet boundary conditions, it turnsout that there exists a critical exponent p = 1+2/N such that blow-up ofpositive solutions always occurs for subcritical exponents, whereas in thesupercritical case global existence can occur for small non-negative initialdata.

The Fujita phenomenon in exterior domains under the Robin boundary conditions