Finite element approximation of sparse parabolic control problems
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Identificadores
URI: http://hdl.handle.net/10902/12165DOI: 10.3934/mcrf.2017014
ISSN: 2156-8472
ISSN: 2156-8499
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2017-09Derechos
© American Institute of Mathematical Sciences. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Mathematical Control and Related Fields following peer review. The definitive publisher-authenticated version, Mathematical Control and Related Fields, 2017, 7(3), 393-417 is available online at: http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=14341
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Mathematical Control and Related Fields, 2017, 7(3), 393-417
Editorial
American Institute of Mathematical Sciences
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Palabras clave
Optimal control
Semilinear parabolic equations
Sparse solutions
Finite element approximation
Error estimates
Resumen/Abstract
We study the finite element approximation of an optimal control problem governed by a semilinear partial differential equation and whose objective function includes a term promoting space sparsity of the solutions. We prove existence of solution in the absence of control bound constraints and provide the adequate second order sufficient conditions to obtain error estimates. Full discretization of the problem is carried out, and the sparsity properties of the discrete solutions, as well as error estimates, are obtained.
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