| 4n-2阶发展方程的算子半群 |
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| 引用本文： | 张利勋,刘永智,王康宁,欧中华,代志勇,彭增寿. 4n-2阶发展方程的算子半群[J]. 电子科技大学学报(自然科学版), 2005, 34(4): 559-561 |
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| 作者姓名： | 张利勋 刘永智 王康宁 欧中华 代志勇 彭增寿 |
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| 作者单位： | 1.电子科技大学光电信息学院 成都 610054; |
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| 摘 要： | 针对高价发展方程的形式解,将二阶发展方程扩展为时滞分布参数系统标准型中的4n-2阶发展方程,同时构造内积形成4n-2维Hilbert空间。将4n-2阶发展方程转化为一阶发展方程组,求得4n-2阶发展方程的生成算子和在一定的条件下生成半群。构造出半群的结构式并证明其具有的基本特征。当n=1时为二阶发展方程型的Golstein算子半群。
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| 关 键 词： | 半群 生成算子 Hilbert空间 时滞分布参数系统 |
| 收稿时间： | 2003-04-22 |
| 修稿时间： | 2003-04-22 |
Operator Semigroup of 4n-2 Order Evolution Equations |
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| ZHANG Li-xun,LIU Yong-zhi,WANG Kang-ning,OU Zhong-hua,DAI Zhi-Yong,PENG Zeng-shou. Operator Semigroup of 4n-2 Order Evolution Equations[J]. Journal of University of Electronic Science and Technology of China, 2005, 34(4): 559-561 |
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| Authors: | ZHANG Li-xun LIU Yong-zhi WANG Kang-ning OU Zhong-hua DAI Zhi-Yong PENG Zeng-shou |
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| Affiliation: | 1.School of Optic-Electronic Information,UEST of China Chengdu 610054;2.School of Applied Mathematics,UEST of China Chengdu 610054 |
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| Abstract: | In allusion to the form solution to high order evolution equation, 4n-2 order evolution equation that is one of the best important standard type about time-delay distributed parameter system expand from two order evolution equation and construct the inner product to become 4n-2 dimension Halberd space at the same time. The generating operator of 4n-2 order evolution equation is obtained and it generates a semigroup when 4n-2 order evolution equation is changed into one order evolution equation set. The configuration form's semigroup is constructed and it's basic character is proved. In particular, the semigroup(n=1) intitules Golstein's. |
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| Keywords: | semigroup generating operator Halberd space time-delay distributed parameter system |
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