TY - JOUR

T1 - Blow-up set for a semilinear heat equation with small diffusion

AU - Fujishima, Yohei

AU - Ishige, Kazuhiro

PY - 2010/9

Y1 - 2010/9

N2 - We consider the blow-up problem for a semilinear heat equation, where Ω is a domain in RN, N≥1, ε{lunate}>0, p>1, and T>0. In this paper, under suitable assumptions on {φε{lunate}}, we prove that, if the family of the solutions {uε{lunate}} satisfies a uniform type I blow-up estimate with respect to ε{lunate}, then the solution uε{lunate} blows up only near the maximum points of the initial datum φε{lunate} for any sufficiently small ε{lunate}>0. This is proved without any conditions on the exponent p and the domain Ω, such as (N-2)p<N+2 and the convexity of the domain Ω.

AB - We consider the blow-up problem for a semilinear heat equation, where Ω is a domain in RN, N≥1, ε{lunate}>0, p>1, and T>0. In this paper, under suitable assumptions on {φε{lunate}}, we prove that, if the family of the solutions {uε{lunate}} satisfies a uniform type I blow-up estimate with respect to ε{lunate}, then the solution uε{lunate} blows up only near the maximum points of the initial datum φε{lunate} for any sufficiently small ε{lunate}>0. This is proved without any conditions on the exponent p and the domain Ω, such as (N-2)p<N+2 and the convexity of the domain Ω.

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U2 - 10.1016/j.jde.2010.03.028

DO - 10.1016/j.jde.2010.03.028

M3 - Article

AN - SCOPUS:77952957932

VL - 249

SP - 1056

EP - 1077

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 5

ER -