The Hoff Equations on a Graph with the Multipoint Initial-Final Value Condition

S.A. Zagrebina, South Ural State University, E.A. Soldatova, South Ural State University
2019 Journal of Computational and Engineering Mathematics  
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
more » ... tion 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.
doi:10.14529/jcem190205 fatcat:uwvg6emljfei5pmf3pfq3i7mye