Geodesic
The Hoff equations on a graph with the multipoint initial-final value condition
Journal of computational and engineering mathematics, Tome 6 (2019) no. 2, pp. 54-63.

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We consider the Hoff equations on a graph. For these equations, we prove the unique solvability of the multipoint initial-final value problem, and construct an analytical solution. As an example, we consider the Hoff equations on a double-edge graph with a three-point initial-final value condition. The article, in addition to the introduction and bibliography, contains two parts. The first part presents theoretical information about Sobolev type equations, as well as construction of a solution to an abstract Sobolev type equation with the multipoint initial-final value condition. In the second part, we apply the obtained abstract results to a specific Hoff model.
Keywords: Sobolev type equations, relatively bounded operator, multipoint initial-final value condition, Hoff model on a graph. 
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     author = {S. A. Zagrebina and E. A. Soldatova},
     title = {The {Hoff} equations on a graph with the multipoint initial-final value condition},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/JCEM_2019_6_2_a4/}
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S. A. Zagrebina; E. A. Soldatova. The Hoff equations on a graph with the multipoint initial-final value condition. Journal of computational and engineering mathematics, Tome 6 (2019) no. 2, pp. 54-63. http://geodesic.mathdoc.fr/item/JCEM_2019_6_2_a4/