On the blowup of multidimensional semilinear heat equations. (English) Zbl 0815.35039

This paper is concerned with positive, blowing-up solutions of the semilinear heat equation \(u_ t - \Delta u = u^ p\) in \(\mathbb{R}^ n \times (0,T)\), \(p > 1\). The refined asymptotics for \(u\) in a backward space-time parabola near a blowup point are calculated and the properties concerning the local structure of the blowup set are obtained.
Reviewer: J.Diblík (Brno)


35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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