Blow-up profile of a solution for a nonlinear heat equation with small diffusion

Hiroki Yagisita, Masanobu Kaneko

研究成果: ジャーナルへの寄稿記事

12 引用 (Scopus)

抄録

This paper is concerned with positive solutions of semilinear diffusion equations ut = ε2 Δ u + up in Ω with small diffusion under the Neumann boundary condition, where p > 1 is a constant and Ω is a bounded domain in RN with C2 boundary. For the ordinary differential equation ut = up, the solution u0 with positive initial data u0 ∈ C(Ω) has a blow-up set S0 = (x ∈ Ω|u0(x) = maxyeΩ u0(y)) and a blowup profile u0 *(x)=(u0(x)-(p-1) - (maxyeΩ u0(y))-(p-1))-1/(p-1) outside the blow-up set S0. For the diffusion equation ut = ε2 Δ u + up in Ω under the boundary condition ∂u/∂v = 0 on ∂Ω, it is shown that if a positive function u0 ∈ C2(Ω) satisfies ∂u0/∂v = 0 on ∂Ω, then the blow-up profile uε *(x) of the solution uε with initial data u0 approaches u0 *(x) uniformly on compact sets of Ω \ S0 as ε → +0.

元の言語英語
ページ(範囲)993-1005
ページ数13
ジャーナルJournal of the Mathematical Society of Japan
56
発行部数4
DOI
出版物ステータス出版済み - 1 1 2004

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Blow-up Set
Nonlinear Heat Equation
Diffusion equation
Blow-up
Semilinear Equations
Neumann Boundary Conditions
Compact Set
Positive Solution
Bounded Domain
Ordinary differential equation
Boundary conditions
Profile

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Blow-up profile of a solution for a nonlinear heat equation with small diffusion. / Yagisita, Hiroki; Kaneko, Masanobu.

:: Journal of the Mathematical Society of Japan, 巻 56, 番号 4, 01.01.2004, p. 993-1005.

研究成果: ジャーナルへの寄稿記事

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