Abstract:
Linear and nonlinear inverse problems for the nonstationary multispeed anisotropic kinetic transport equation are studied. Sufficient conditions for the existence and uniqueness of weak solutions to these problems in various function spaces are found. The proofs of the corresponding theorems imply that solutions of the inverse problems under study can be obtained by applying the method of successive approximations.
Key words:
inverse problem, nonstationary multispeed anisotropic kinetic transport equation, existence and uniqueness theorem, weak solution, method of successive approximations.
Citation:
N. P. Volkov, “Solvability of certain inverse problems for the nonstationary kinetic transport equation”, Zh. Vychisl. Mat. Mat. Fiz., 56:9 (2016), 1622–1627; Comput. Math. Math. Phys., 56:9 (2016), 1598–1603
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\by N.~P.~Volkov
\paper Solvability of certain inverse problems for the nonstationary kinetic transport equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 9
\pages 1622--1627
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\crossref{https://doi.org/10.7868/S0044466916090167}
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\transl
\jour Comput. Math. Math. Phys.
\yr 2016
\vol 56
\issue 9
\pages 1598--1603
\crossref{https://doi.org/10.1134/S0965542516090153}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10454
https://www.mathnet.ru/eng/zvmmf/v56/i9/p1622
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I V Prokhorov, I P Yarovenko, “Computed tomography imaging using a short pulse source with angular discontinuity”, J. Phys.: Conf. Ser., 1715:1 (2021), 012043
I. V. Prokhorov, I. P. Yarovenko, “Determination of the attenuation coefficient for the nonstationary radiative transfer equation”, Comput. Math. Math. Phys., 61:12 (2021), 2088–2101
A. V. Baskakov, N. P. Volkov, “Refinement of the reactor dynamics mathematical model”, VII International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019, 012006
A. V. Baskakov, N. P. Volkov, “On some control problems of dynamic of reactor”, VI International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012005
N. P. Volkov, “Linear inverse problem of the reactor dynamics”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012061
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