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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
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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:
- 1.
- N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1985. MR 1009162 (90g:47001a)
- 2.
- H. Gajewski and K. Zacharias, Zur Regularisierung einer Klasse nichtkorrekter Probleme bel Evolutionsgleichungen, J. Math. Anal. Appl. 38(1972), 784-789. MR 0308625 (46:7739)
- 3.
- V. K. Ivanov, I. V. Mel'nikova and A.I. Filinkov, Differential Operator Equations and Ill-posed Problems, Nauka, Moscow, 1995. (In Russian) MR 1415388 (97j:47092)
- 4.
- R. Lattes and J.-L. Lions, The Method of Quasi-reversibility Applications to Partial Differential Equations, Amer. Elsevier Publ. Co., New York, 1969. MR 0243746 (39:5067)
- 5.
- R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Springer-Verlag, Berlin, 1994. MR 1290783 (96b:47047)
- 6.
- I. V. Mel'nikova, General theory of the ill-posed Cauchy problem, J. Inverse and Ill-posed Problems 3(1995), 149-171. MR 1341036 (97a:34156)
- 7.
- I. V. Mel'nikova and A.I. Filinkov, Abstract Cauchy Problems: Three Approaches, Chapman and Hall, London, 2001. MR 1823612 (2002h:34110)
- 8.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983. MR 0710486 (85g:47061)
- 9.
- R. E. Showalter, The final problem for evolution equations, J. Math. Anal. Appl. 47(1974), 563-572. MR 0352644 (50:5131)
- 10.
- A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-posed Problems, Winston and Sons, Washington D.C., 1977. MR 0455365 (56:13604)
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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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