| 半线性抛物型方程组解的爆破条件及爆破速率 |
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| 引用本文： | 薛应珍,容跃堂,王文海. 半线性抛物型方程组解的爆破条件及爆破速率[J]. 纺织高校基础科学学报, 2006, 19(4): 337-340 |
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| 作者姓名： | 薛应珍 容跃堂 王文海 |
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| 作者单位： | 西安工程大学,理学院,陕西,西安,710048 |
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| 摘 要： | 研究了带有齐次Dirichlet边界条件,反应项为非线性局部化热源的半线性抛物型方程组正解的爆破条件及爆破速率问题.首先,利用Souplet方法得到了方程组中两个分量同时爆破的必要条件和一个充分条件,然后,在此基础上建立了解的一致爆破速率估计.最后,通过验证得到Souplet方法在这类方程中是十分有效的.
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| 关 键 词： | 抛物型方程组 非线性局部热源 同时爆破 爆破速率估计 |
| 文章编号： | 1006-8341（2006）04-0337-04 |
| 收稿时间： | 2006-05-15 |
| 修稿时间： | 2006-05-15 |
The conditions of simultaneous blow up and blasting rate estimates of solutions for semi-linear parabolic systems |
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| XUE Ying-zhen,RONG Yue-tang,WANG Wen-hai. The conditions of simultaneous blow up and blasting rate estimates of solutions for semi-linear parabolic systems[J]. Basic Sciences Journal of Textile Universities, 2006, 19(4): 337-340 |
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| Authors: | XUE Ying-zhen RONG Yue-tang WANG Wen-hai |
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| Abstract: | The blasting conditions and blasting rate estimates of positive solutions to semi-linear parabolic systems with nonlinear localized sources are studied in the paper,subjected to null Dirichlet boundary conditions.At first,by the Souplet method,the necessary condition and the sufficient condition for which two components blow up simultaneously are obtained,and then the uniform blasting rate estimate is established.Finally,that Souplet method was tested in this type of equation is very effective. |
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| Keywords: | parabolic systems nonlinear localized heat sources simultaneously blow up blasting rate estimate |
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