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- W2006755174 abstract "This paper is concerned with blowup of positive solutions to a Cauchy problem for a parabolic–elliptic system { U t = ∇ ⋅ ( ∇ U − U ∇ V ) in R N × ( 0 , T ) , 0 = Δ V + U in R N × ( 0 , T ) . We say that a solution ( U , V ) blows up at t = T if lim sup t → T | U ( t ) | ∞ = ∞ with L ∞ -norm | ⋅ | ∞ in R N . When a solution ( U , V ) blows up at t = T , the blowup is called of type I if lim sup t → T ( T − t ) | U ( t ) | ∞ < ∞ and of type II otherwise. It was shown in Herrero and Velázquez (1996) [12] and Mizoguchi and Senba (2007) [20] that there exist radial type II blowup solutions for N = 2 or N ⩾ 11 . When 3 ⩽ N ⩽ 9 , type II blowup solutions were given by formal analysis in Brenner et al. (1999) [2] and Herrero et al. (1997) [10] . We give a sufficient condition for a solution to exhibit type I blowup in the case of 3 ⩽ N ⩽ 9 ." @default.
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- W2006755174 date "2011-01-01" @default.
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- W2006755174 title "A sufficient condition for type I blowup in a parabolic–elliptic system" @default.
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- W2006755174 doi "https://doi.org/10.1016/j.jde.2010.10.016" @default.
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