| 带非局部源的退化半线性抛物型方程解的爆破 |
| |
| 引用本文： | 栗付才,刘其林,谢春红.带非局部源的退化半线性抛物型方程解的爆破[J].数学学报,2003,46(2):391-396. |
| |
| 作者姓名： | 栗付才 刘其林 谢春红 |
| |
| 作者单位： | 南京大学数学系,南京,210093 |
| |
| 摘 要： | 该文研究带Dirichlet边界条件的退化半线性抛物型方程:xqut-uxx=∫0af(u)dx,这里q>0.作者证明了局部解的存在唯一性并且得到当初值充分大时解在有限时刻爆破.进而,证明解的爆破点集是整个区间0,a],这与具有局部源的方程解的性质不同.
|
| 关 键 词： | 退化半线性抛物型方程 非局部源 爆破 爆破点集 |
| 文章编号： | 0583-1431(2003)02-0391-06 |
| 修稿时间： | 2000年6月18日 |
Blow-Up for Degenerate Semiliuear Parabolic Equations with Nonlocal Source |
| |
| Fu Cai LI Qi Lin LIU Chun Hong XIE.Blow-Up for Degenerate Semiliuear Parabolic Equations with Nonlocal Source[J].Acta Mathematica Sinica,2003,46(2):391-396. |
| |
| Authors: | Fu Cai LI Qi Lin LIU Chun Hong XIE |
| |
| Institution: | Fu Cai LI Qi Lin LIU Chun Hong XIE (Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China) |
| |
| Abstract: | In this paper, we investigate degenerate semilinear parabolic equations xqut -uxx= f0a f(u)dx with Dirichlet boundary condition and q > 0. It is proved that the local solution is existent and unique and the solution blows up in a finite time provided that the initial data u0(x) is sufficiently large. Furthermore, it is shown that the blowup set is the entire interval 0, a], which is quite different from the results for the solution with local source. |
| |
| Keywords: | Degenerate semilinear parabolic equation Nonlocal source Bow-up Blowup set |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
|
