Abstract
Boundary value problems of thermal conductivity on a star graph are considered, inspired by engineering applications, e.g., heat conduction phenomena in mesh-like structures. Based on the generalized function method, a unified technique for solving boundary value problems of heat conduction has been developed. Generalized solutions to transient and stationary boundary value problems are constructed for several types of boundary conditions at the ends, with the generalized Kirchhoff conditions at the node. Using the symmetry properties of the Fourier transform of the fundamental solution, regular integral representations of solutions to boundary value problems are obtained. The derived results allow simulation of heat sources of various types, including those involving singular generalized functions. The employed method of generalized functions enables tackling a wide class of boundary value problems, including those with local and connected boundary conditions at the ends of the graph, and various transmission conditions at the node.