Decay rates for elastic-thermoelastic star-shaped networks

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dc.contributor.authorHan, Z.-J.
dc.contributor.authorZuazua, Enrique
dc.date.accessioned2026-01-16T08:35:00Z
dc.date.available2026-01-16T08:35:00Z
dc.date.issued2017-09
dc.date.updated2026-01-16T08:35:00Z
dc.description.abstractThis work discusses the asymptotic behaviour of a transmission problem on star-shaped networks of interconnected elastic and thermoelastic rods. Elastic rods are undamped, of conservative nature, while the thermoelastic ones are damped by thermal effects. We analyse the overall decay rate depending of the number of purely elastic components entering on the system and the irrationality properties of its lengths. First, a sufficient and necessary condition for the strong stability of the thermoelastic-elastic network is given. Then, the uniform exponential decay rate is proved by frequency domain analysis techniques when only one purely elastic undamped rod is present. When the network involves more than one purely elastic undamped rod the lack of exponential decay is proved and nearly sharp polynomial decay rates are deduced under suitable irrationality conditions on the lengths of the rods, based on Diophantine approximation arguments. More general slow decay rates are also derived. Finally, we present some numerical simulations supporting the analytical results.en
dc.description.sponsorshipThe first author was supported by the Natural Science Foundation of China grant NSFC-61573252 and China Scholarship Council. The second author was supported by the Advanced Grant DYCON of the European Research Council Executive Agency, ICON of the ANR-2016-ACHN-0014-01 (France), FA9550-14-1-0214 of the EOARD-AFOSR, FA9550-15-1-0027 of AFOSR, the MTM2014-52347 Grant of the MINECO and a Humboldt Research Award at the University of Erlangen-Nurnbergen
dc.identifier.citationHan, Z.-J., & Zuazua, E. (2017). Decay rates for elastic-thermoelastic star-shaped networks. Networks and Heterogeneous Media, 12(3), 461-488. https://doi.org/10.3934/NHM.2017020
dc.identifier.doi10.3934/NHM.2017020
dc.identifier.eissn1556-181X
dc.identifier.issn1556-1801
dc.identifier.urihttps://hdl.handle.net/20.500.14454/4726
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences
dc.rights© American Institute of Mathematical Sciences
dc.subject.otherThermoelasticity
dc.subject.otherElasticity
dc.subject.otherRods
dc.subject.otherStar-shaped network
dc.subject.otherExponential decay
dc.subject.otherPolynomial decay
dc.subject.otherAsymptotic behavior
dc.subject.otherResolvent estimates
dc.subject.otherIrrationality conditions
dc.titleDecay rates for elastic-thermoelastic star-shaped networksen
dc.typejournal article
dcterms.accessRightsopen access
oaire.citation.endPage488
oaire.citation.issue3
oaire.citation.startPage461
oaire.citation.titleNetworks and Heterogeneous Media
oaire.citation.volume12
oaire.versionVoR
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