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Title: A simple regularization method for the ill-posed evolution equation (English)
Author: Tuan, Nguyen Huy
Author: Trong, Dang Duc
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 61
Issue: 1
Year: 2011
Pages: 85-95
Summary lang: English
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Category: math
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Summary: The nonhomogeneous backward Cauchy problem $$u_t +Au(t) = f(t),\quad u(T) = \varphi$$, where $A$ is a positive self-adjoint unbounded operator which has continuous spectrum and $f$ is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar. (English)
Keyword: nonlinear parabolic problem
Keyword: backward problem
Keyword: semigroup of operators
Keyword: ill-posed problem
Keyword: contraction principle
MSC: 35K05
MSC: 35K99
MSC: 47H10
MSC: 47J06
idZBL: Zbl 1224.35165
idMR: MR2782761
DOI: 10.1007/s10587-011-0019-9
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Date available: 2011-05-23T12:33:17Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/141520
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