Geodesic
Fokas method for the heat equation on metric graphs
Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 766-782

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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. 
@article{CMFD_2021_67_4_a8,
     author = {Z. A. Sobirov and M. R. Eshimbetov},
     title = {Fokas method for the heat equation on metric graphs},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {766--782},
     publisher = {mathdoc},
     volume = {67},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a8/}
}
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Z. A. Sobirov; M. R. Eshimbetov. Fokas method for the heat equation on metric graphs. Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 766-782. http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a8/