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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 19, Issue 4-5 (Jan 2011)


On the approximations of derivatives of integrated semigroups. II

Miao Li / Vladimir Morozov / Sergey Piskarev
Published Online: 2011-09-26 | DOI: https://doi.org/10.1515/jiip.2011.053


This paper is devoted to the regularization in the process of approximation of values of unbounded operators in Banach spaces. More precisely, we consider the approximations of unbounded generators of C 0-semigroups and integrated semigroups. We consider M. M. Lavrentiev's method. Some iterative procedures are also investigated. It is shown that in general Banach spaces the approximation of the values of unbounded operators converges in strong sense. The presentation is given in the abstract framework of the discrete approximation scheme, which includes finite element methods, finite difference schemes and projection methods.

Keywords.: Abstract differential equations; Banach spaces; C 0-semigroups; integrated semigroups; Trotter–Kato theorem; discretization methods; discrete semigroups; stability of difference schemes; Lavrentiev's method; regularization procedure; iterative methods; ill-posed problems

About the article

Received: 2011-05-05

Revised: 2011-05-11

Published Online: 2011-09-26

Published in Print: 2011-11-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.053.

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