Fokas Method for the Heat Equation on Metric Graphs

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Abstract

The paper presents a method for constructing solutions to initial-boundary value problems for the heat equation on simple metric graphs such as a star-shaped graph, a tree, and a triangle with three converging edges. The solutions to the problems are constructed by the so-called Fokas method, which is a generalization of the Fourier transform method. In this case, the problem is reduced to a system of algebraic equations for the Fourier transform of the unknown values of the solution at the vertices of the graph.

About the authors

Z. A. Sobirov

National University of Uzbekistan named after M. Ulugbek

Author for correspondence.
Email: z.sobirov@nuu.uz
Tashkent, Uzbekistan

M. R. Eshimbetov

National University of Uzbekistan named after M. Ulugbek

Email: mr.eshimbetov92@gmail.com
Tashkent, Uzbekistan

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