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Regularization for a class of ill-posed Cauchy problems
Author(s):
Yongzhong
Huang;
Quan
Zheng
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3005-3012.
MSC (2000):
Primary 47A52;
Secondary 47D06, 34G10
Posted:
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  in a Banach space. Our main result is that if  is the generator of an analytic semigroup of angle  , 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.
References:
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- 2.
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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:
10.1090/S0002-9939-05-07822-6
PII:
S 0002-9939(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
Posted:
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
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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