Fila, Marek; Velázquez, Juan J. L.; Winkler, Michael Grow-up on the boundary for a semilinear parabolic problem. (English) Zbl 1090.35034 Chipot, Michel (ed.) et al., Nonlinear elliptic and parabolic problems. A special tribute to the work of Herbert Amann, Zürich, Switzerland, June 28–30, 2004. Basel: Birkhäuser (ISBN 3-7643-7266-4/hbk). Progress in Nonlinear Differential Equations and their Applications 64, 137-150 (2005). The authors consider the problem \[ \begin{alignedat}{2} u_t&= u_{xx}- pu^{2p-1},\quad &0&< x< 1,\;t>0,\\ -u_x&= u^p, &x&= 0,\\ u_x&= 0, &x&=1,\\ u|_{t=0}&= u_0(x)\geq 0, &0&\leq x\leq 1, \end{alignedat} \] where \(p> 1\). They study the growth rate of these global unbounded solutions as \(t\to\infty\). The authors find their growth rate at the singular point on the boundary.For the entire collection see [Zbl 1077.00009]. Reviewer: Messoud A. Efendiev (Berlin) Cited in 3 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations Keywords:growth rate; singular point; semilinear parabolic problem; one space dimension PDFBibTeX XMLCite \textit{M. Fila} et al., Prog. Nonlinear Differ. Equ. Appl. 64, 137--150 (2005; Zbl 1090.35034) Full Text: DOI