Using sparse control methods to identify sources in linear diffusion-convection equations

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URI: http://hdl.handle.net/10902/18250
ISSN: 1361-6420
ISSN: 0266-5611
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Autoría
Casas Rentería, EduardoAutoridad Unican; Kunisch, Karl
Fecha
2019-10-03
Derechos
© IOP Publishing. This is an author-created, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6420/ab331c
Publicado en
Inverse Problems, 2019, 35(11), 114002
Editorial
Institute of Physics Publishing
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Palabras clave
Measure controls
Sparsity
Parabolic equations
Source identification
Resumen/Abstract
Techniques from sparse control theory are proposed to approximate initial conditions for diffusion-convection equations. Existence and uniqueness of optimal controls are proven, and necessary and sufficient optimality conditions are derived. From these conditions the sparsity structure of the solutions is derived, which relates to identification of the sources to be reconstructed.
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