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

Kulaev R. Ch.
Vladikavkaz Mathematical Journal 2011. Vol. 13. Issue 3.

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.

Keywords: differential equation on the graph, the circuit integral method.

The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses.