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 Ufimsk. Mat. Zh., 2012, Volume 4, Issue 2, Pages 114–126 (Mi ufa152)

On solutions of the first-order PDE with a multidimensional symmetric integral and their modelling

F. S. Nasyrov, E. V. Yureva

Ufa State Aviation Technical University, Ufa, Russia

Abstract: The deterministic analog of the multidimensional Stratonovich integral is constructed. Method of solution of a system of equations with a multidimensional symmetric integral is elaborated. The method of characteristics for solving the Cauchy problem for first-order partial differential equations with a multidimensional symmetric integral is developed. This method reduces solving the initial-value problem of the above equations to solving a system of equations with a multidimensional symmetric integral.

Keywords: multidimensional symmetric integral, differential equations system with multidimensional symmetric integral, partial differential equations with multidimensional symmetric integral, the method of characteristics.

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Bibliographic databases:

UDC: 519.2

Citation: F. S. Nasyrov, E. V. Yureva, “On solutions of the first-order PDE with a multidimensional symmetric integral and their modelling”, Ufimsk. Mat. Zh., 4:2 (2012), 114–126

Citation in format AMSBIB
\Bibitem{NasYur12} \by F.~S.~Nasyrov, E.~V.~Yureva \paper On solutions of the first-order PDE with a~multidimensional symmetric integral and their modelling \jour Ufimsk. Mat. Zh. \yr 2012 \vol 4 \issue 2 \pages 114--126 \mathnet{http://mi.mathnet.ru/ufa152} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3432648}