dc.contributor.author | Balehowsky, Tracey | |
dc.contributor.author | Kujanpää, Antti | |
dc.contributor.author | Lassas, Matti | |
dc.contributor.author | Liimatainen, Tony | |
dc.date.accessioned | 2022-09-15T06:56:19Z | |
dc.date.available | 2022-09-15T06:56:19Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Balehowsky, 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.other | CONVID_156520596 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/83258 | |
dc.description.abstract | We 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.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Springer | |
dc.relation.ispartofseries | Communications in Mathematical Physics | |
dc.rights | In Copyright | |
dc.subject.other | Boltzmannin yhtälö | |
dc.subject.other | Boltzmann equation | |
dc.title | An Inverse Problem for the Relativistic Boltzmann Equation | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202209154603 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Inversio-ongelmien huippuyksikkö | fi |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Centre of Excellence in Inverse Problems | en |
dc.contributor.oppiaine | Mathematics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 983-1049 | |
dc.relation.issn | 0010-3616 | |
dc.relation.numberinseries | 3 | |
dc.relation.volume | 396 | |
dc.type.version | acceptedVersion | |
dc.rights.copyright | © 2022 Springer | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 309963 | |
dc.relation.grantnumber | 312121 | |
dc.subject.yso | inversio-ongelmat | |
dc.subject.yso | tiiviin aineen fysiikka | |
dc.subject.yso | hiukkasfysiikka | |
dc.subject.yso | yhtälöt | |
dc.subject.yso | matematiikka | |
dc.subject.yso | mallintaminen | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p27912 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p38692 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p15576 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p3553 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p3160 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p3533 | |
dc.rights.url | http://rightsstatements.org/page/InC/1.0/?language=en | |
dc.relation.doi | 10.1007/s00220-022-04486-8 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundingprogram | Centre of Excellence, AoF | en |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundingprogram | Huippuyksikkörahoitus, SA | fi |
jyx.fundinginformation | The 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.okm | A1 | |