摘要
该文研究了如下柯西问题ut=uxx + (t+ 1) -σ/2 | x| σ| u| p -1| u| , x∈ R,t∈ R+ ,u(x ,0 ) =u0 (x) , x∈ R.其中参数 σ≥ 0 ,u0 (x)在 R上 k次变号 ,满足某种速降条件 .证明了 :如果 max{ σ,1} <p≤ 1+ 2k+ 1,那么所有非零解在有限时间内爆破 ;如果 p>max{ σ,1+ 2k+
In this paper,we are concerned with the global existence and blowup of sign changing solutions to certain class of reaction diffusion equations. Consider the following Cauchy problem \$\$u\-t=u\-\{xx\}+(t+1)\+\{-σ/2\}|x|\+σ|u|\+\{p-1\}u,\ x∈R, t∈R\++, u(x,0)=u\-0(x),\ x∈R.\$\$where \$σ≥0, p>1\$. \; It is shown that , for any nonnegative integer \$k,p\-k=1+2/(k+1)\$ is the critical exponent for the above problem,i.e.\; If \$\%max\%(σ,1)<p≤p\-k\$,then any nontrivial solution with \$u\-0(x)∈H\+1\-ρ∩∑\-k\$ blows up in finite time.\; If \$p>\%max\%(σ,p\-k)\$, then there exists a global solution with \$u\-0(x)∈H\+1\-ρ∩∑\-k\$.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2002年第2期150-156,共7页
Acta Mathematica Scientia
基金
国家自然科学基金资助项目
