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Bulletin of the MRSU / Section "Physics and mathematics" / 2013 № 1.

 

Baskakov A.V., Volkov N.P.

ON SOME CONDITIONS FOR THE EXISTENCE OF CONTROL PROBLEMS FOR THE TIME-DEPENDENT KINETIC TRANSPORT EQUATION // Bulletin of the Moscow Regional State University (electronic journal) [Bulletin of the Moscow Regional State University (electronic journal)]. 2013. no. 1.


UDC Index: 517.958, 62.50

Date of publication: 30.01.2013

The full text of the article

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Abstract


In the article linear and nonlinear control problems for the time-dependent multi-speed anisotropic kinetic transport equation are considered. The author found sufficient conditions for the existence and uniqueness of the generalized solutions of the investigated problems in various functional spaces. By proving the corresponding theorems it was shown that solutions of the investigated control problems can be obtained by the method of successive approximations.

Key words


control problem, time-dependent multi-speed anisotropic kinetic transport equation, unique existence theorem, generalized solution, method of successive approximations

List of references


1. Tihonov A.N., Arsenin V.Ja., Timonov A.A. Matematicheskie zadachi komp'juternoj tomografii. - M.: Nauka, 1987.
2. Marchuk G.I. Metody rascheta jadernyh reaktorov. M.: Gosatomizdat, 1961.
3. Prilepko A.I., Volkov N.P. Obratnye zadachi opredelenija parametrov nestacionarnogo kineticheskogo uravnenija perenosa po dopolnitel'noj informacii o sledah iskomoj funkcii // Differencial'nye uravnenija, 1988. - Tom 24. - № 1.
4. Volkov N.P. On Some Inverse Problems for Time-Dependent Transport Equation // ILL-Posed Problems in Natural Sciences. - Moscow: TVP-VSP, 1992.

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