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- W2043336675 abstract "We consider the blow-up problem of a semilinear heat equation, u t = D Δ u + u p in Ω × ( 0 , T D ) , ∂ u ∂ ν ( x , t ) = 0 on ∂ Ω × ( 0 , T D ) , u ( x , 0 ) = φ ( x ) ⩾ 0 in Ω , where Ω is a bounded smooth domain in R N , T D > 0 , D > 0 , and p > 1 . We study the blow-up time, the location of the blow-up set, and the blow-up profile of the blow-up solution for sufficiently large D . In particular, we prove that, for almost all initial data φ , if D is sufficiently large, then the solution blows-up only near the maximum points of the orthogonal projection of the initial data φ from L 2 ( Ω ) onto the second Neumann eigenspace." @default.
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- W2043336675 date "2005-05-01" @default.
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- W2043336675 title "Blow-up problems for a semilinear heat equation with large diffusion" @default.
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- W2043336675 doi "https://doi.org/10.1016/j.jde.2004.10.021" @default.
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