Mu, Chunlai; Zeng, Rong Single-point blow-up for a doubly degenerate parabolic equation with nonlinear source. (English) Zbl 1223.35089 Proc. R. Soc. Edinb., Sect. A, Math. 141, No. 3, 641-654 (2011). The authors consider positive solutions of the Cauchy problem for the doubly degenerate equation \[ u_t-\text{div}(|\nabla u^m|^\sigma\nabla u^m)=u^\beta, \quad \text{for } x\in\mathbb R^N,\;t>0, \]where \(\sigma>0\), \(m>1\), \(\beta>m(1+\sigma)\), \(N\geq1\). The authors study the set of blow-up points and the behavior of \(u\) at the blow-up point. They prove single-point blow-up for a large class of radial decreasing solutions. The upper and lower estimates of the blow-up solution near the single blow-up point are also obtained. Reviewer: Yuanyuan Ke (Beijing) Cited in 3 Documents MSC: 35B44 Blow-up in context of PDEs 35K65 Degenerate parabolic equations 35B09 Positive solutions to PDEs 35K59 Quasilinear parabolic equations Keywords:radial decreasing solutions PDFBibTeX XMLCite \textit{C. Mu} and \textit{R. Zeng}, Proc. R. Soc. Edinb., Sect. A, Math. 141, No. 3, 641--654 (2011; Zbl 1223.35089) Full Text: DOI