One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations
One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations
复制标题
半线性热方程奇异N维解的一维行为
DOI：
10.1007/s002200100589
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发表时间：
2002
影响因子：
2.4
通讯作者：
H. Zaag
中科院分区：
文献类型：
--
作者：
H. Zaag
我们考虑 u(x,t) 的解 ut=Δu+|u|p− 1u 在时间 T 爆炸，其中 u:ℝN×[0,T)→ℝ,p>1, (N−2)p<N+2 且 u(0)≥ 0 或 (3N−4)p<3N+8。我们关注非孤立爆炸点附近解的行为，即 T−t→ 0。在非简并条件下，假设爆炸集是局部连续的且为 N−1 维，我们避开变量 T−t 的对数尺度，并以小得多的误差项 (T−t)1, 1/2−η 给出解的更尖锐的展开，对于任何 η > 0。特别地，如果另外p>3，则该解非常接近作为到爆炸组的距离的函数的一维解的叠加。最后，我们证明，爆炸集是连续的这一假设意味着它是 C1, 1/2−η（对于任何 η>0）。
We consideru(x,t) a solution ofut=Δu+|u|p− 1uthat blows up at timeT, whereu:ℝN×[0,T)→ℝ,p>1, (N−2)p<N+2 and eitheru(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, asT−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous andN−1 dimensional, we escape logarithmic scales of the variableT−tand give a sharper expansion of the solution with the much smaller error term (T−t)1, 1/2−ηfor any η>0. In particular, if in additionp>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it isC1, 1/2−ηfor any η>0.
影响因子：
1.7
作者：
Brenner, MP;Constantin, P;Venkataramani, SC
通讯作者：
Venkataramani, SC