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 Mathematical notes of NEFU, 2017, Volume 24, Issue 1, Pages 57–73 (Mi svfu6)

Mathematics

Formulas for an explicit solution of the model nonlocal problem associated with the ordinary transport equation

I. V. Tikhonova, V. N. Son Tungb

a Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskyie Gory, Moscow 119991, Russia
b Mathematical Analysis Department, Moscow State University of Education, 14, Krasnoprudnaya Street, Moscow 107140, Russia

Abstract: A specific nonlocal problem for the multidimesional ordinary transport equation is studied. An additional condition for the time averages is given. The theorem of existence and uniqueness of solution is obtained. We show that the solution could be found constructively, explicitly, and in a finite number of iterations.

Keywords: transport equation, nonlocal problem, resolving formula.

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UDC: 517.95

Citation: I. V. Tikhonov, V. N. Son Tung, “Formulas for an explicit solution of the model nonlocal problem associated with the ordinary transport equation”, Mathematical notes of NEFU, 24:1 (2017), 57–73

Citation in format AMSBIB
\Bibitem{TikSon17} \by I.~V.~Tikhonov, V.~N.~Son Tung \paper Formulas for an explicit solution of the model nonlocal problem associated with the ordinary transport equation \jour Mathematical notes of NEFU \yr 2017 \vol 24 \issue 1 \pages 57--73 \mathnet{http://mi.mathnet.ru/svfu6} \elib{http://elibrary.ru/item.asp?id=30353129}