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Internal observability for coupled systems of linear partial differential equations

hal.structure.identifier
dc.contributor.authorLissy, Pierre*
hal.structure.identifier
dc.contributor.authorZuazua, Enrique
HAL ID: 10801		*
dc.date.accessioned2017-12-05T12:18:19Z
dc.date.available2017-12-05T12:18:19Z
dc.date.issued2019
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17171
dc.language.isoenen
dc.subjectpartial differential equations
dc.subjectsystems
dc.subjectobservability inequalities
dc.subjectrank conditions
dc.subject.ddc515en
dc.titleInternal observability for coupled systems of linear partial differential equations
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe deal with the internal observability for some coupled systems of partial differential equations with constant or time-dependent coupling terms by means of a reduced number of observed components. We prove new general observability inequalities under some Kalman-like or Silverman-Meadows-like condition. Our proofs combine the observability properties of the underlying scalar equation with algebraic manipulations. In the more specific case of systems of heat equations with constant coefficients and non-diagonalizable diffusion matrices, we also give a new necessary and sufficient condition for ob-servability in the natural L 2-setting. The proof relies on the use of the Lebeau-Robbiano strategy together with a precise study of the cost of controllability for linear ordinary differential equations , and allows to treat the case where each component of the system is observed in a different subdomain.
dc.relation.isversionofjnlnameSIAM Journal on Control and Optimization
dc.relation.isversionofjnlvol57
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2019
dc.relation.isversionofjnlpages832-853
dc.relation.isversionofdoihttps://doi.org/10.1137/17M1119160
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01480301
dc.subject.ddclabelAnalyseen
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-12-15T14:54:27Z
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