Abstract
The transport equation with an unknown right-hand side is considered on a compact Riemannian manifold. The right-hand side of this equation is recovered from values of the outcoming flow. Assumptions under which the solution of the inverse problem is unique are formulated.
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References
D. V. Finch, “Uniqueness for the attenuated X-ray transform in the physical range,”Inverse Problems,2, No. 2, 197–203 (1986).
V. A. Sharafutdinov, “Inverse problem for determining a source in the stationary transport equation for a refraction medium,”Sib. Mat. Zh.,35, No. 4, 937–945 (1994).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 236–242.
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Sharafutdinov, V.A. The inverse problem of determining the source in the stationary transport equation on a riemannian manifold. J Math Sci 96, 3430–3433 (1999). https://doi.org/10.1007/BF02172822
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DOI: https://doi.org/10.1007/BF02172822