The Fujita phenomenon in exterior domains under the Robin boundary conditions

Details The Fujita phenomenon in exterior domains under the Robin boundary conditions The Fujita phenomenon in exterior domains under the Robin boundary conditions

2010-10-07

arxiv.org/abs/1010.1443v1

Mathematics

Analysis of PDEs

9 pages

Scientific paper

The Fujita phenomenon for nonlinear parabolic problems dtu = \deltau + 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.

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