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The Fujita phenomenon in exterior domains under dynamical boundary conditions. (English) Zbl 1185.35016

The paper studies the Fujita phenomenon for nonlinear parabolic equations of the type
\[ \partial_tu=\Delta u+u^p \]
in an exterior domain of \(\mathbb R^N\) under dissipative dynamical boundary conditions
\[ \sigma\partial_tu+ \partial_\nu u=0. \]
It is proved that, as happens in the case of Dirichlet boundary conditions, that there is 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.

MSC:

35B33 Critical exponents in context of PDEs
35K58 Semilinear parabolic equations
35B44 Blow-up in context of PDEs
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