Al Sayed, Waad; Véron, Laurent Solutions of some nonlinear parabolic equations with initial blow-up. (English) Zbl 1221.35072 Alvino, Angelo (ed.) et al., On the notions of solution to nonlinear elliptic problems: results and developments. Caserta: Dipartimento di Matematica, Seconda Università di Napoli; Rome: Aracne (ISBN 978-88-548-3032-5/hbk). Quaderni di Matematica 23, 2-23 (2008). The authors study the solvability of a semilinear parabolic equation in \(N\)-dimensional bounded domains with initial blow-up. Under the assumption that the boundary is compact and satisfies the parabolic Wiener criterion, the existence and uniqueness of a positive solution is shown.For the entire collection see [Zbl 1203.35007]. Reviewer: Cheng He (Beijing) Cited in 3 Documents MSC: 35B44 Blow-up in context of PDEs 35K58 Semilinear parabolic equations 35K20 Initial-boundary value problems for second-order parabolic equations 35B09 Positive solutions to PDEs Keywords:parabolic Wiener criterion PDFBibTeX XMLCite \textit{W. Al Sayed} and \textit{L. Véron}, Quad. Mat. 23, 2--23 (2008; Zbl 1221.35072) Full Text: arXiv