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Zbl 1171.35059
Souplet, Philippe
Single-point blow-up for a semilinear parabolic system. (English)
[J] J. Eur. Math. Soc. (JEMS) 11, No. 1, 169-188 (2009). ISSN 1435-9855; ISSN 1435-9863/e

The authors study the positive solutions of a semilinear parabolic system coupled by power nonlinearilities in a ball or in the whole space. A single-point blow-up result is proved for a large class of radial decreasing solutions, which answer the open problem posed by {\it A. Friedman} and {\it Y. Giga} [J. Fac. Sci., Univ. Tokyo, Sect. I A 34, 65--79 (1987; Zbl 0648.35042)]. Finally, the author obtain the lower pointwise estimates for the final blow-up profiles.
[Cheng He (Beijing)]

MSC 2000:: *35K50 Systems of parabolic equations, boundary value problems
35B40 Asymptotic behavior of solutions of PDE
35K35 Higher order parabolic equations, boundary value problems
35K57 Reaction-diffusion equations

Keywords: positive solutions; semilinear parabolic system; nonlinearities; blow-up set; single point blow-up

Citations: Zbl 0648.35042

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