TY - JOUR
T1 - Location of blow-up set for a semilinear parabolic equation with large diffusion
AU - Ishige, Kazuhiro
AU - Mizoguchi, Noriko
PY - 2003/11/1
Y1 - 2003/11/1
N2 - This paper is concerned with {ut = DΔu + up in Ω × (0, TD), (P) ∂u/∂v (x, t) = 0 on ∂Ω × (0, TD), u (x, 0) = φ(x) ≥ 0 in Ω, where Ω is a bounded smooth domain in RN, TD > 0, D > 0, and p > 1 with (N-2) p ≤ N+2. Let P2 be the projection from L2(Ω) onto the second Neumann eigenspace. We prove that, if P2φ ≢ 0 in Ω and D is sufficiently large, the solution u of (P) blows up only near the set M ∪ ∂Ω, where script M sign = {x ∈ Ω̄: (P2φ)(x) = maxy∈Ω̄(P2φ)(y)}.
AB - This paper is concerned with {ut = DΔu + up in Ω × (0, TD), (P) ∂u/∂v (x, t) = 0 on ∂Ω × (0, TD), u (x, 0) = φ(x) ≥ 0 in Ω, where Ω is a bounded smooth domain in RN, TD > 0, D > 0, and p > 1 with (N-2) p ≤ N+2. Let P2 be the projection from L2(Ω) onto the second Neumann eigenspace. We prove that, if P2φ ≢ 0 in Ω and D is sufficiently large, the solution u of (P) blows up only near the set M ∪ ∂Ω, where script M sign = {x ∈ Ω̄: (P2φ)(x) = maxy∈Ω̄(P2φ)(y)}.
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U2 - 10.1007/s00208-003-0463-4
DO - 10.1007/s00208-003-0463-4
M3 - Article
AN - SCOPUS:0345414147
VL - 327
SP - 487
EP - 511
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 3
ER -