Boundary Value Problems on a Star Thermal Graph and their Solutions
Alexeyeva L.A. Dadayeva A.N. Prikazchikov D.A. Ainakeyeva N.Zh.
2025E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2025#118Issue 24 - 15 pp.
In this study, heat conductivity boundary value problems 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 on such graphs is developed. Generalized solutions to transient and stationary boundary value problems are constructed for different conditions at the end edges, with the Kirchhoff conditions at the common node. Regular integral representations of solutions to boundary value problems are obtained using the properties and symmetry of the fundamental solution’s Fourier transform. The derived results allow the action of various heat sources to be simulated, including concentrated ones by using singular generalized functions. The generalized function method enables a wide variety of boundary value problems to be tackled, including those with local boundary conditions at the ends of the graph, and various transmission conditions at the common node. Based on the research, the authors propose an analytical solution method under the action of various heat sources to solve various boundary value problems on a star thermal graph.
boundary equations , Fourier transform , generalized functions method , generalized solution , heat flow , star graph , temperature , transmission conditions
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Joldasbekov Institute of Mechanics and Engineering, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Kazakh National Research Technical University named after K.I. Satpayev, Almaty, Kazakhstan
Keele University, Staffordshire, United Kingdom
Narxoz University, Almaty, Kazakhstan
Joldasbekov Institute of Mechanics and Engineering
Institute of Mathematics and Mathematical Modeling
Kazakh National Research Technical University named after K.I. Satpayev
Keele University
Narxoz University
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