Open AccessFokas Method for the Heat Equation on Metric Graphs
Author(s) -
Z. A. Sobirov,
M. R. Eshimbetov
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-4-766-782
Subject(s) - mathematics , fourier transform , generalization , algebraic equation , metric (unit) , boundary value problem , graph , heat equation , mathematical analysis , discrete mathematics , physics , operations management , quantum mechanics , nonlinear system , economics
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.