An Inverse Problem for the Relativistic Boltzmann Equation
Balehowsky, T., Kujanpää, A., Lassas, M., & Liimatainen, T. (2022). An Inverse Problem for the Relativistic Boltzmann Equation. Communications in Mathematical Physics, 396(3), 983-1049. https://doi.org/10.1007/s00220-022-04486-8
Julkaistu sarjassa
Communications in Mathematical PhysicsPäivämäärä
2022Oppiaine
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsTekijänoikeudet
© 2022 Springer
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.
Julkaisija
SpringerISSN Hae Julkaisufoorumista
0010-3616Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/156520596
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Suomen AkatemiaRahoitusohjelmat(t)
Akatemiahanke, SA; Huippuyksikkörahoitus, SALisätietoja rahoituksesta
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.Lisenssi
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