Li, Gang; Huang, Yu Global existence and quenching phenomena for a parabolic equation of the mean curvature type with nonlinear convection term. (Chinese. English summary) Zbl 1066.35046 Appl. Math., Ser. A (Chin. Ed.) 19, No. 4, 417-425 (2004). Summary: The paper studies the first initial-boundary value problem in a bounded domain in \(\mathbb{R}^n\) for the mean curvature equation with a nonlinear convection term: \(u_t-\text{div}\{\sigma (|\nabla u|^2)\nabla u\}+b(u)\cdot \nabla u=0\). The existence of the weak solution is derived and the quenching phenomena and the \(L^\infty\)-estimate to the solution are given. MSC: 35K65 Degenerate parabolic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) Keywords:first initial-boundary value problem; nonlinear convection term; \(L^\infty\)-estimate PDFBibTeX XMLCite \textit{G. Li} and \textit{Y. Huang}, Appl. Math., Ser. A (Chin. Ed.) 19, No. 4, 417--425 (2004; Zbl 1066.35046)