dc.contributor.author Ou, Y. dc.contributor.author Zhu, P. dc.date.accessioned 2017-02-21T08:18:18Z dc.date.available 2017-02-21T08:18:18Z dc.date.issued 2013-12-31 dc.identifier.issn 1468-1218 dc.identifier.uri http://hdl.handle.net/20.500.11824/526 dc.description.abstract In this article we study, by the vanishing viscosity method, the sensitivity analysis of an optimal control problem for 1-D scalar conservation laws in the presence of shocks. It is reduced to investigate the vanishing viscosity limit for the nonlinear conservation law, the corresponding linearized equation and its adjoint equation, respectively. We employ the method of matched asymptotic expansions to construct approximate solutions to those equations. It is then proved that the approximate solutions, respectively, satisfy those viscous equations in the asymptotic sense, and converge to the solutions of the corresponding inviscid problems with certain convergent rates. A new equation for the variation of shock positions is derived. It is also discussed how to identify descent directions to find the minimizer of the viscous optimal control problem in the quasi-shock case. dc.format application/pdf dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Conservation laws dc.subject Optimal control dc.subject Sensitivity dc.subject Shocks dc.subject Vanishing viscosity limit dc.title The vanishing viscosity method for the sensitivity analysis of an optimal control problem of conservation laws in the presence of shocks dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1016/j.nonrwa.2013.02.001 dc.relation.publisherversion https://www.scopus.com/inward/record.uri?eid=2-s2.0-84876414720&doi=10.1016%2fj.nonrwa.2013.02.001&partnerID=40&md5=a38162e8d82f8480e9658feb3f5132fa dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/publishedVersion en_US dc.journal.title Nonlinear Analysis: Real World Applications en_US
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