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Minimumnormprobleme und Zeitoptimale Steuerungen

Title data

Lempio, Frank:
Minimumnormprobleme und Zeitoptimale Steuerungen.
In: Collatz, Lothar ; Werner, H. ; Meinardus, Günter (ed.): Numerische Methoden der Approximationstheorie : Numerical Methods of Approximation Theory; Vortragsauszüge der Tagung über numerische Methoden der Approximationstheorie vom 25. bis 31. Mai 1975 im Mathematischen Forschungsinstitut Oberwolfach (Schwarzwald). - Basel : Birkhäuser , 1976 . - pp. 277-298 . - (International Series of Numerical Mathematics ; 30 ) (Numerische Methoden der Approximationstheorie ; 3)
ISBN 978-3-7643-0824-7
DOI: https://doi.org/10.1007/978-3-0348-7692-6_14

Review:

Abstract in another language

We consider special boundary control systems for parabolic differential equations where the target set is described by a convex body of continuous functions. In this paper we are mainly interested in time-optimal control problems.

Our first approach to these problems is the usual one which allows us to sharpen a bang-bang-principle recently proved by WECK. Here we make use of the same analyticity arguments used already by GLASHOFF for control problems with fixed time interval.

Our second approach consists in embedding the time-optimal control problem into a family of minimum norm problems with general operator restrictions. We investigate these minimum norm problems by means of a characterization theorem for abstract approximation problems, and we believe that this approach will be useful not only for the special problems treated in this paper but also for more general situations.

Further data

Item Type: Article in a book
Refereed: Yes
Subject classification: Mathematics Subject Classification Code: 49A20
Institutions of the University: 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 > Former Professors
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Result of work at the UBT: No
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 12 Feb 2021 08:10
Last Modified: 23 Mar 2021 09:13
URI: https://eref.uni-bayreuth.de/id/eprint/63018