×

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)

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
PDFBibTeX XMLCite
Full Text: arXiv