Blowup for ut=Δu+|delu|2u from Rn into Rm

被引：0
|
作者：
Hirata, D [1 ]
机构：
[1] Sci Univ Tokyo, Fac Sci & Technol, Dept Math, Chiba 2788510, Japan
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 133卷 / 06期
关键词：
blowup; parabolic system; Cauchy problem;
D O I：
10.1090/S0002-9939-05-07821-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we consider the global regularity of smooth solutions u = (u(1),..., u(m)) to the vector-valued Cauchy problem u(t) = Delta u + |del u|(2)u in R-n x [0,infinity), u(x, 0) = u(0)(x) in R-n. We show that if n, m >= 3, the gradient-blowup phenomenon occurs in finite time for suitably chosen u0 vanishing at infinity. We also present a simple example of the L-infinity-blowup solutions for |u(0)| = 1 + epsilon for any epsilon > 0, if m >= 2.
引用
收藏
页码：1823 / 1827
页数：5
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