| 完全二阶抽象柯西问题的温和C-存在族和解空间 |
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| 引用本文： | 高明杵. 完全二阶抽象柯西问题的温和C-存在族和解空间[J]. 系统科学与数学, 2001, 21(1): 033-038 |
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| 作者姓名： | 高明杵 |
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| 作者单位： | 山西师范大学数学与计算机系, |
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| 基金项目： | 国家自然科学基金,山西自然科学基金资助课题. |
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| 摘 要： | 本文中,我们定义了完全二阶抽象柯西问题的温和C-存在族.对指数有界的温和C-存在族,我们还给出了温和C-存在族的Hille-Yosida型的充要条件.对不完全二阶抽象柯西问题,我们定义了解空间和Hille-Yosida空间,我们还证明了不完全二阶抽象柯西问题在其Hille-Yosida空间上是自动适定的,把deLaubenfels文中关于一阶抽象柯西问题的相应结果推广到了二阶的情形.
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| 关 键 词： | 温和C-存在族 二阶抽象柯西问题 解空间 Hille-Yosida空间. |
| 修稿时间： | 1997-09-12 |
MILD C-EXISTENCE FAMILIES AND SOLUTION SPACES OF COMPLETELY SECOND ORDER ABSTRACT CAUCHY PROBLEMS |
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| Gao Mingchu. MILD C-EXISTENCE FAMILIES AND SOLUTION SPACES OF COMPLETELY SECOND ORDER ABSTRACT CAUCHY PROBLEMS[J]. Journal of Systems Science and Mathematical Sciences, 2001, 21(1): 033-038 |
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| Authors: | Gao Mingchu |
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| Affiliation: | Department of Mathematics and Computer Science, Shanxi Teachers University, Linfen 041004,P.R.China |
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| Abstract: | Cauchy problems, and mild C-existence families Hille-Yosida type sufficient and necessary condition for exponential bounded mild C-existence families. We also give the definitions of solution space and Hille-Yosida space for noncompletely abstract Cauchy problems and show that noncompletely abstract Cauchy problems on its Hille-Yosida space is automatically wellposed, which generalizes deLaubenfels's corresponding results on first ordern- abstract Cauchy problems to second order abstract Cauchy problems. |
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| Keywords: | C-existence families second order abstract Cauchy problems solution space Hille-Yosida space. |
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