Payne, L. E.; Schaefer, P. W. Bounds for blow-up time for the heat equation under nonlinear boundary conditions. (English) Zbl 1184.35077 Proc. R. Soc. Edinb., Sect. A, Math. 139, No. 6, 1289-1296 (2009). Summary: A differential inequality technique is used to determine a lower bound on the blow-up time for solutions to the heat equation subject to a nonlinear boundary condition when blow-up of the solution does occur. In addition, a sufficient condition which implies that blow-up does occur is determined. Cited in 48 Documents MSC: 35B44 Blow-up in context of PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations Keywords:differential inequality technique PDFBibTeX XMLCite \textit{L. E. Payne} and \textit{P. W. Schaefer}, Proc. R. Soc. Edinb., Sect. A, Math. 139, No. 6, 1289--1296 (2009; Zbl 1184.35077) Full Text: DOI