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Scattering problems for symmetric systems with dissipative boundary conditions

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPETKOV, Vesselin
dc.date.accessioned2024-04-04T02:19:23Z
dc.date.available2024-04-04T02:19:23Z
dc.date.created2013-02-07
dc.date.issued2013
dc.identifier.isbn978-1-4614-6347-4
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189396
dc.description.abstractEnWe study symmetric systems with dissipative boundary conditions. The solutions of the mixed problems for such systems are given by a contraction semigroup $V(t)f = e^{tG_b}f, t \geq 0$. The solutions $u(t, x) = V(t)f$, where $f$ is an eigenfunction of the generator $G_b$ with eigenvalue $\lambda,\Re \lambda < 0,$ are called asymptotically disappearing (ADS). We prove that the wave operators are not complete if there exist (ADS). This is the case for Maxwell system with special boundary conditions in the exterior of the sphere. We obtain a representation of the scattering kernel and we examine the inverse back-scattering problem related to the leading term of the scattering kernel.
dc.language.isoen
dc.publisherBirkhäuser
dc.source.titleStudies in Phase Space Analysis with Applications to PDEs
dc.subject.endissipative boundary conditions
dc.subject.enasymptotically disappearing solutions
dc.subject.eninverse scattering problems
dc.title.enScattering problems for symmetric systems with dissipative boundary conditions
dc.typeChapitre d'ouvrage
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halPhysique [physics]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.identifier.arxiv1206.3017
bordeaux.page337-353
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.title.proceedingStudies in Phase Space Analysis with Applications to PDEs
hal.identifierhal-00950069
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00950069v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.btitle=Studies%20in%20Phase%20Space%20Analysis%20with%20Applications%20to%20PDEs&amp;rft.date=2013&amp;rft.spage=337-353&amp;rft.epage=337-353&amp;rft.au=PETKOV,%20Vesselin&amp;rft.isbn=978-1-4614-6347-4&amp;rft.genre=unknown


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