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Single-point blow-up for a doubly degenerate parabolic equation with nonlinear source. (English) Zbl 1223.35089

The authors consider positive solutions of the Cauchy problem for the doubly degenerate equation

u t -div(|u m | σ u m )=u β ,forx N ,t>0,

where σ>0, m>1, β>m(1+σ), N1. 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.

MSC:
35B44Blow-up (PDE)
35K65Parabolic equations of degenerate type
35B09Positive solutions of PDE
35K59Quasilinear parabolic equations