Volume 22, Number 2, April-June 2016
|Page(s)||355 - 370|
|Published online||04 March 2016|
Parabolic control problems in space-time measure spaces∗
Departmento de Matemática Aplicada y Ciencias de la Computación,
E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria,
2 Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria
3 Radon Institute, Austrian Academy of Sciences, 69 Alterberger Stra β e, 4040 Linz, Austria
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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