Ding, Juntang; Guo, Bao-Zhu Global and blow-up solutions for nonlinear parabolic equations with a gradient term. (English) Zbl 1243.35028 Houston J. Math. 37, No. 4, 1265-1277 (2011). Authors’ abstract: “This paper studies a Neumann initial-boundary value problem for a nonlinear parabolic equation with a gradient term in a bounded domain in the \(N\)-dimensional Euclidean space with \(N\geq2\) and a smooth boundary. By using upper and lower solutions, existence of a global positive solution \(u\), an upper estimate of \(u\), blowup of \(u\), and an upper bound of the blow-up time are investigated. For illustrations, two examples are given.” Reviewer: Chiu Yeung Chan (Lafayette) Cited in 4 Documents MSC: 35B44 Blow-up in context of PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35K55 Nonlinear parabolic equations Keywords:nonlinear parabolic equation; gradient term; global solution; blow-up solution; upper and lower solutions; global positive solution; upper estimate PDFBibTeX XMLCite \textit{J. Ding} and \textit{B.-Z. Guo}, Houston J. Math. 37, No. 4, 1265--1277 (2011; Zbl 1243.35028) Full Text: Link