Galaktionov, Victor A.; Vazquez, Juan L. Continuation of blowup solutions of nonlinear heat equations in several space dimensions. (English) Zbl 0874.35057 Commun. Pure Appl. Math. 50, No. 1, 1-67 (1997). Equations of the form \[ u_t=\Delta (u^m)\pm u^p,\qquad x\in\mathbb{R}^N,\;t>0 \] are studied. For the positive sign and \(p>1\), the solutions may blow up in finite time. For the negative sign and \(p<1\), extinction may occur in the sense that initially positive solutions vanish at some point in finite time. The possible continuation of solutions after the appearence of singularities is investigated. A classification is obtained in terms of the exponents \(m>0\) and \(p\). Some questions that had been open for a long time are answered here. It is obvious that the methods used in the paper have wider applicability. Reviewer: M.Fila (Bratislava) Cited in 3 ReviewsCited in 160 Documents MSC: 35K65 Degenerate parabolic equations 35B60 Continuation and prolongation of solutions to PDEs 35B40 Asymptotic behavior of solutions to PDEs 35K55 Nonlinear parabolic equations 35K15 Initial value problems for second-order parabolic equations Keywords:extinction PDFBibTeX XMLCite \textit{V. A. Galaktionov} and \textit{J. L. Vazquez}, Commun. Pure Appl. Math. 50, No. 1, 1--67 (1997; Zbl 0874.35057) Full Text: DOI