The Fujita phenomenon in exterior domains under the dynamical boundary conditions

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

2010-10-08

arxiv.org/abs/1010.1608v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

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.

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