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Zbl 1223.35089
Mu, Chunlai; Zeng, Rong
Single-point blow-up for a doubly degenerate parabolic equation with nonlinear source.
(English)
[J] Proc. R. Soc. Edinb., Sect. A, Math. 141, No. 3, 641-654 (2011). ISSN 0308-2105; ISSN 1473-7124/e

The authors consider positive solutions of the Cauchy problem for the doubly degenerate equation $$u_t-\text{div}(|\nabla u^m|^\sigma\nabla u^m)=u^\beta, \quad \text {for } x\in\Bbb R^N,\ t>0,$$ where $\sigma>0$, $m>1$, $\beta>m(1+\sigma)$, $N\ge1$. 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.
[Yuanyuan Ke (Beijing)]
MSC 2000:
*35B44
35K65 Parabolic equations of degenerate type
35B09
35K59

Keywords: radial decreasing solutions

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