This article is cited in 2 papers

Computational Mathematics

The Hoff equations on a graph with the multipoint initial-final value condition

S. A. Zagrebina, E. A. Soldatova

South Ural State University, Chelyabinsk, Russian Federation

Abstract: 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.

UDC: 517.9

MSC: 35R02

Received: 10.01.2019

Language: English

DOI: 10.14529/jcem190205