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dc.contributor.authorBalehowsky, Tracey
dc.contributor.authorKujanpää, Antti
dc.contributor.authorLassas, Matti
dc.contributor.authorLiimatainen, Tony
dc.date.accessioned2022-09-15T06:56:19Z
dc.date.available2022-09-15T06:56:19Z
dc.date.issued2022
dc.identifier.citationBalehowsky, T., Kujanpää, A., Lassas, M., & Liimatainen, T. (2022). An Inverse Problem for the Relativistic Boltzmann Equation. <i>Communications in Mathematical Physics</i>, <i>396</i>(3), 983-1049. <a href="https://doi.org/10.1007/s00220-022-04486-8" target="_blank">https://doi.org/10.1007/s00220-022-04486-8</a>
dc.identifier.otherCONVID_156520596
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/83258
dc.description.abstractWe consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime (M, g) with an unknown metric g. We consider measurements done in a neighbourhood V⊂M of a timelike path μ that connects a point x− to a point x+. The measurements are modelled by a source-to-solution map, which maps a source supported in V to the restriction of the solution to the Boltzmann equation to the set V. We show that the source-to-solution map uniquely determines the Lorentzian spacetime, up to an isometry, in the set I+(x−)∩I−(x+)⊂M. The set I+(x−)∩I−(x+) is the intersection of the future of the point x− and the past of the point x+, and hence is the maximal set to where causal signals sent from x− can propagate and return to the point x+. The proof of the result is based on using the nonlinearity of the Boltzmann equation as a beneficial feature for solving the inverse problem.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesCommunications in Mathematical Physics
dc.rightsIn Copyright
dc.subject.otherBoltzmannin yhtälö
dc.subject.otherBoltzmann equation
dc.titleAn Inverse Problem for the Relativistic Boltzmann Equation
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202209154603
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineInversio-ongelmien huippuyksikköfi
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineCentre of Excellence in Inverse Problemsen
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange983-1049
dc.relation.issn0010-3616
dc.relation.numberinseries3
dc.relation.volume396
dc.type.versionacceptedVersion
dc.rights.copyright© 2022 Springer
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber309963
dc.relation.grantnumber312121
dc.subject.ysoinversio-ongelmat
dc.subject.ysotiiviin aineen fysiikka
dc.subject.ysohiukkasfysiikka
dc.subject.ysoyhtälöt
dc.subject.ysomatematiikka
dc.subject.ysomallintaminen
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p27912
jyx.subject.urihttp://www.yso.fi/onto/yso/p38692
jyx.subject.urihttp://www.yso.fi/onto/yso/p15576
jyx.subject.urihttp://www.yso.fi/onto/yso/p3553
jyx.subject.urihttp://www.yso.fi/onto/yso/p3160
jyx.subject.urihttp://www.yso.fi/onto/yso/p3533
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1007/s00220-022-04486-8
dc.relation.funderResearch Council of Finlanden
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundinginformationThe authors were supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Modelling and Imaging, Grant numbers 312121 and 309963) and AtMath Collaboration project.
dc.type.okmA1


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