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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.

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Authors and Affiliations

  1. National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan

    Z. A. Sobirov & M. R. Eshimbetov

Authors
  1. Z. A. Sobirov
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  2. M. R. Eshimbetov
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Correspondence to Z. A. Sobirov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 4, Science — Technology — Education — Mathematics — Medicine, 2022.

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Sobirov, Z.A., Eshimbetov, M.R. Fokas Method for the Heat Equation on Metric Graphs. J Math Sci 278, 530–545 (2024). https://doi.org/10.1007/s10958-024-06936-1

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  • DOI: https://doi.org/10.1007/s10958-024-06936-1

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