# 李刚,于勇.半线性抛物方程可变号解的全局存在和爆破[J].东南大学学报(自然科学版),2005,35(5):829-832.[doi:10.3969/j.issn.1001-0505.2005.05.037] 　Li Gang,Yu Yong.Global existence and blow-up of sign-changing solutions to semilinear parabolic equations[J].Journal of Southeast University (Natural Science Edition),2005,35(5):829-832.[doi:10.3969/j.issn.1001-0505.2005.05.037] 点击复制 半线性抛物方程可变号解的全局存在和爆破( ) 分享到： var jiathis_config = { data_track_clickback: true };

35

2005年第5期

829-832

2005-09-20

## 文章信息/Info

Title:
Global existence and blow-up of sign-changing solutions to semilinear parabolic equations

Author(s):
Department of Mathematics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Keywords:

O175.26
DOI:
10.3969/j.issn.1001-0505.2005.05.037

Abstract:
The equation: ut=uxx+(1+t)q|u|p-1u/|x|σ1 is considered, where σ≥0,q>σ/2-1, bound value being equal to zero, initial value being nonincreasing. Firstly, a self-similar transformation is made, then its eigenvalue problem is considered, energy function E(s) is defined, some existing inequalities are used, and the theory of infinite dimensional dynamical systems is adopted. It is shown that for any nonnegative integer k, k is the number of initial value sing-changing in bounded domain D,pk=1+(2+2q-σ)/(k+1) is the critical exponent for the above problem, i.e, if 1<p≤pk, then any nontrivial solution blows up at finite time; if p>pk, then the problem has a global solution.