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Regularization for a class of ill-posed Cauchy problems


Authors: Yongzhong Huang and Quan Zheng
Journal: Proc. Amer. Math. Soc. 133 (2005), 3005-3012
MSC (2000): Primary 47A52; Secondary 47D06, 34G10
DOI: https://doi.org/10.1090/S0002-9939-05-07822-6
Published electronically: March 31, 2005
MathSciNet review: 2159779
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Abstract: This paper is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator $A$ in a Banach space. Our main result is that if $-A$ is the generator of an analytic semigroup of angle $\ge\pi/4$, then there exists a family of regularizing operators for such an ill-posed Cauchy problem by using the Gajewski and Zacharias quasi-reversibility method, and semigroups of linear operators.


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Additional Information

Yongzhong Huang
Affiliation: Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
Email: huang5464@hotmail.com

Quan Zheng
Affiliation: Department of Mathematics and Center for Optimal Control and Discrete Mathematics, Huazhong Normal University, Wuhan 430079, People’s Republic of China – and – Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
Email: qzheng@hust.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-05-07822-6
Keywords: Ill-posed Cauchy problem, quasi-reversibility, regularizing family, analytic semigroup
Received by editor(s): December 11, 2003
Received by editor(s) in revised form: May 18, 2004
Published electronically: March 31, 2005
Additional Notes: This project was supported by TRAPOYT, the National Science Foundation of China (Grant No.10371046)
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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