| WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS |
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| 作者姓名： | 黄永忠 郑权 |
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| 作者单位： | Department of Mathematics Huazhong University of Science and Technology Wuhan 430074，China，School of Mathematics and statistics，Huazhong Normal University，Wuhan 430079，China Department of Mathematics Huazhong University of Science and Technology，Wuhan 430074，China |
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| 基金项目： | This project was supported by TRAPOYT, the Key Project of Chinese Ministry of Education(104126) the NNSF of China(10371046) |
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| 摘 要： | This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibility method and regularized semigroups. Finally, an example is given.
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| 关 键 词： | Cauchy问题 准可逆性 弱调整算子 部分能量 规则半群 |
| 收稿时间： | 2004-08-21 |
WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS |
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| Huang Yongzhong, Zheng Quan.WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS[J].Acta Mathematica Scientia,2006,26(3):483-490. |
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| Authors: | Huang Yongzhong Zheng Quan |
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| Abstract: | This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibility method and regularized semigroups. Finally, an example is given. |
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| Keywords: | Ill-posed Cauchy problem quasi-reversibility family of weakly regularizing operators fractional power regularized semigroup |
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