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arXiv · 1010.1608

The Fujita phenomenon in exterior domains under the dynamical boundary conditions

Jean-François Rault
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Abstract

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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Jean-François Rault. 2010-10-08. The Fujita phenomenon in exterior domains under the dynamical boundary conditions. https://arxiv.org/abs/1010.1608

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