Zhang, Hailiang; Zhang, Wu Blow-up rate of positive solution of uniformly parabolic equations with nonlinear boundary conditions. (English) Zbl 1047.35069 Ann. Differ. Equations 19, No. 3, 439-444 (2003). Summary: This paper deals with the blow-up of positive solutions of the uniformly parabolic equations \(u_t= Lu+ a(x) f(u)\) subject to nonlinear Neumann boundary conditions \({\partial u\over\partial n}+ b(x)g(u)= 0\). Under suitable assumptions on nonlinear functions \(f\), \(g\) and initial data \(u_0(x)\), the blow-up of the solutions in a finite time is proved by the maximum principles. Moreover, the bounds of “blow-up time” and blow-up rate are obtained. MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35K55 Nonlinear parabolic equations 37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:maximum principle; Neumann boundary conditions PDFBibTeX XMLCite \textit{H. Zhang} and \textit{W. Zhang}, Ann. Differ. Equations 19, No. 3, 439--444 (2003; Zbl 1047.35069)