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An extended mathematical framework for barrier methods in function space

Title data

Schiela, Anton:
An extended mathematical framework for barrier methods in function space.
In: Bercovier, Michel ; Gander, Martin J. ; Kornhuber, Ralf ; Widlund, Olof (Hrsg.): Domain decomposition methods in science and engineering XVIII. - Berlin, Heidelberg : Springer , 2009 . - pp. 201-208 . - (Lecture Notes in Computational Science and Engineering ; 70 )
ISBN 973-595-031-6
DOI: https://doi.org/10.1007/978-3-642-02677-5_21

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Project information

Project title:
Project's official titleProject's id
DFG Research Center Matheon "Mathematics for key technologies"FZT 86

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

In this note, we extend the mathematical framework in [7] of barrier methods for state constrained optimal control problems with PDEs to a more general setting. In [7] we modelled the state equation by Ly = u with L a closed, densely defined, surjective operator. This restricts the applicability of our theory mainly to certain distributed control problems. Motivated by the discussion in [6], we consider in this work operator equations of the more general form Ay-Bu = 0, where A is closed, densely defined and with closed range and B is continuous. While this change in framework only neccessitates minor modificatios in the theory, it extends its applicability to large additional classes of control problems, such as boundary control and finite dimensional control. To make this paper as self contained as possible, assumptions and results of [7] are recapitulated, but for brevity proofs and more detailed information are only given when there are differences to [7]. This is possible, because our extension has only a very local effect.

Further data

Item Type: Article in a book
Refereed: Yes
Additional notes: A preliminary version is published at the Konrad-Zuse-Zentrum für Informationstechnik, Berlin as ZIB-Report 08-07.
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Mar 2015 08:21
Last Modified: 25 Mar 2015 08:46
URI: https://eref.uni-bayreuth.de/id/eprint/8082