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A concise proof for existence and uniqueness of solutions of linear parabolic PDEs in the context of optimal control

Title data

Schiela, Anton:
A concise proof for existence and uniqueness of solutions of linear parabolic PDEs in the context of optimal control.
In: Systems & Control Letters. Vol. 62 (October 2013) Issue 10 . - pp. 895-901.
ISSN 0167-6911
DOI: https://doi.org/10.1016/j.sysconle.2013.06.013

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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

We present a concise proof for existence and uniqueness of solutions of linear parabolic PDEs. It is based on an analysis of the corresponding differential operator and its adjoint in appropriate spaces and simple enough to be presented in the context of an introductory lecture on optimal control of PDEs. Our approach also clarifies some aspects in the structure of first order optimality conditions as illustrated at an example.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: A preliminary version is published at the Preprint series of the Institute of Mathematics, Technische Universität Berlin, Preprint 03-2013.
Keywords: parabolic PDEs; optimal control; existence theory
Subject classification: Mathematics Subject Classification Code: 35K15 (47N20 49K20)
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: 12 Mar 2015 15:12
Last Modified: 12 Mar 2015 15:12
URI: https://eref.uni-bayreuth.de/id/eprint/8041