Rault, Jean-François The Fujita phenomenon in exterior domains under dynamical boundary conditions. (English) Zbl 1185.35016 Asymptotic Anal. 66, No. 1, 1-8 (2010). 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. Reviewer: Dian K. Palagachev (Bari) Cited in 4 Documents MSC: 35B33 Critical exponents in context of PDEs 35K58 Semilinear parabolic equations 35B44 Blow-up in context of PDEs Keywords:global solutions; blow-up of positive solutions PDFBibTeX XMLCite \textit{J.-F. Rault}, Asymptotic Anal. 66, No. 1, 1--8 (2010; Zbl 1185.35016) Full Text: DOI arXiv