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arXiv · 1010.1443

The Fujita phenomenon in exterior domains under the Robin boundary conditions

Jean-François Rault
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Abstract

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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Jean-François Rault. 2010-10-07. The Fujita phenomenon in exterior domains under the Robin boundary conditions. https://arxiv.org/abs/1010.1443

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