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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.
Bd. 62
(2013)
Heft 10
.
- S. 895-901.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2013.06.013
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Offizieller Projekttitel Projekt-ID DFG Research Center Matheon "Mathematics for key technologies" FZT 86 |
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Deutsche Forschungsgemeinschaft |
Abstract
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.