Geodesic
Existence theorem for a parabolic mixed problem on a graph with boundary conditions containing time derivatives
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 139-148
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The initial-boundary value problem is considered for a parabolic equation on a geometric graph with boundary conditions containing a time derivative. The theorem on the existence of a solution of the boundary value problem is established, which allows one to represent solutions as contour integrals.
Keywords: differential equation on a graph, method of contour integral. 
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R. Ch. Kulaev. Existence theorem for a parabolic mixed problem on a graph with boundary conditions containing time derivatives. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 139-148. http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a10/

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