Modified quasi-reversibility method for final value problems in Banach spaces

This paper is concerned with the final value problem associated with a linear operator A in a Banach space, where − A is the generator of a uniformly bounded analytic semigroup. Based on the deLaubenfels' functional calculus, we use new quasi-reversibility method, introduced by Boussetila and R...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-04, Vol.340 (2), p.757-769
Main Author: Huang, Yongzhong
Format: Article
Language:English
Subjects:
Analytic semigroup
Exact sciences and technology
Functional analysis
Functional calculus
Group theory
Group theory and generalizations
Ill-posed problem
Mathematical analysis
Mathematics
Operator theory
Quasi-reversibility
Sciences and techniques of general use
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Summary:This paper is concerned with the final value problem associated with a linear operator A in a Banach space, where − A is the generator of a uniformly bounded analytic semigroup. Based on the deLaubenfels' functional calculus, we use new quasi-reversibility method, introduced by Boussetila and Rebbani recently, to form an approximate problem. We obtain some results in a Banach space similar to those in a Hilbert space.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.09.019