Filtered gradient algorithms for inverse design problems of one-dimensional burgers equation

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dc.contributor.author Gosse, Laurent
dc.contributor.author Zuazua, Enrique
dc.contributor.editor Gosse, Laurent
dc.contributor.editor Natalini, Roberto
dc.contributor.other UAM. Departamento de Matemáticas es_ES
dc.date.accessioned 2019-08-22T11:39:09Z
dc.date.available 2019-08-22T11:39:09Z
dc.date.issued 2017-03-09
dc.identifier.citation Innovative Algorithms and Analysis. Eds. Laurent Gosse, Roberto Natalini. Springer INdAM Series (SINDAMS), 16 (2017): 197-227 en_US
dc.identifier.isbn 978-3-319-49261-2 (print) en_US
dc.identifier.isbn 978-3-319-49262-9 (online) en_US
dc.identifier.uri http://hdl.handle.net/10486/688402
dc.description The final publication is available at Springer via https://doi.org/10.1007/978-3-319-49262-9_7 en_US
dc.description.abstract Inverse design for hyperbolic conservation laws is exemplified through the 1D Burgers equation which is motivated by aircraft’s sonic-boom minimization issues. In particular, we prove that, as soon as the target function (usually a Nwave) isn’t continuous, there is a whole convex set of possible initial data, the backward entropy solution being possibly its centroid. Further, an iterative strategy based on a gradient algorithm involving “reversible solutions” solving the linear adjoint problem is set up. In order to be able to recover initial profiles different from the backward entropy solution, a filtering step of the backward adjoint solution is inserted, mostly relying on scale-limited (wavelet) subspaces. Numerical illustrations, along with profiles similar to F-functions, are presented en_US
dc.description.sponsorship Acknowledgements This work was partially supported by the Advanced Grant 694126-DYCON (Dynamic Control) of the European Research Council Executive Agency, ICON of the French ANR (2016-ACHN-0014-01), FA9550-15-1-0027 of AFOSR, A9550-14-1-0214 of the EOARD-AFOSR, and the MTM2014-52347 Grant of the MINECO (Spain) en_US
dc.format.extent 27 pag. en_US
dc.format.mimetype application/pdf en
dc.language.iso eng en
dc.publisher Springer, Cham en_US
dc.relation.ispartof Innovative Algorithms and Analysis en_US
dc.rights © Springer International Publishing AG 2017 en_US
dc.title Filtered gradient algorithms for inverse design problems of one-dimensional burgers equation en_US
dc.type bookPart en
dc.subject.eciencia Matemáticas es_ES
dc.relation.publisherversion https://doi.org/10.1007/978-3-319-49262-9_7 es_ES
dc.identifier.doi 10.1007/978-3-319-49262-9_7 es_ES
dc.identifier.publicationfirstpage 197 es_ES
dc.identifier.publicationlastpage 227 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/694126/EU//DYCON es_ES
dc.relation.projectID Gobierno de España. MTM2014-52347 es_ES
dc.type.version info:eu-repo/semantics/acceptedVersion en
dc.rights.accessRights openAccess en
dc.authorUAM Zuazua Iriondo, Enrique (260385)


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