STABLE BLOW-UP PATTERNS

被引：39

作者：

BRESSAN, A

机构：

[1] Department of Mathematics, University of Colorado, Boulder

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 1992年 / 98卷 / 01期

关键词：

D O I：

10.1016/0022-0396(92)90104-U

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For the semilinear heat equation ut = Δu + eu in a convex domain Ω ⊂ Rn, given any b ε{lunate} Ω we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u(T, x) ≈ -2 ln |x - b| + ln |ln |x - b|| + ln 8, T being the blow-up time. Using a suitable set of rescaled coordinates, this asymptotic behavior is proved to be stable with respect to small perturbations of the initial conditions. © 1992.

引用

页码：57 / 75

页数：19