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JOURNALS // Vladikavkazskii Matematicheskii Zhurnal // Archive

Vladikavkaz. Mat. Zh., 2011 Volume 13, Number 3, Pages 42–52 (Mi vmj393)

On existence of the solution of parabolic problem on the graph with a boundary conditions, containing derivatives on time

R. Ch. Kulaev

South Mathematical Institute of VSC RAS, Vladikavkaz, Russia

Abstract: The mixed problem for the parabolic equation set on geometrical graph, with boundary conditions containing a derivative on time is considered. The theorem of existence of the solution of the boundary problem giving representation of the solution in the form of circuit integral is established.

Key words: differential equation on the graph, the circuit integral method.

UDC: 517.956

Received: 07.09.2010



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