| Issue |
ESAIM: COCV
Volume 22, Number 2, April-June 2016
|
|
|---|---|---|
| Page(s) | 355 - 370 | |
| DOI | https://doi.org/10.1051/cocv/2015008 | |
| Published online | 04 March 2016 | |
Parabolic control problems in space-time measure spaces∗
1
Departmento de Matemática Aplicada y Ciencias de la Computación,
E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria,
39005
Santander,
Spain
eduardo.casas@unican.es
2
Institute for Mathematics and Scientific Computing, University of
Graz, Heinrichstrasse
36, 8010
Graz,
Austria
karl.kunisch@uni-graz.at
3
Radon Institute, Austrian Academy of Sciences,
69 Alterberger
Stra β e, 4040
Linz,
Austria
Received:
26
May
2014
Revised:
17
November
2014
Optimal control problems in measure spaces governed by parabolic equations with are considered. The controls appear as spatial measure in the initial condition and as space-time measures as forcing functions. First order optimality conditions are derived and certain structural properties, in particular sparsity, are discussed. An framework for approximation if these highly irregular problems is also proposed.
Mathematics Subject Classification: 90C48 / 49J52 / 49K20
Key words: Space-time measure controls / optimal control / sparsity / parabolic equations / first order optimality conditions / numerical approximation
© EDP Sciences, SMAI 2016
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