Semilinear parabolic equations on graphs

Authors

DOI:

https://doi.org/10.31652/3041-1955-2026-03-01-03

Keywords:

partial differential equation, parabolic equation, initial-boundary value problem, connected directed graph, weak solution

Abstract

 The paper considers an initial-boundary value problem for a semilinear parabolic equation on a simple connected directed graph. A weak solution to the problem is defined in the appropriate functional spaces and conditions for continuity and transmission at the graph vertices are provided. The unique solvability of the problem is proved.

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Author Biographies

  • Oleh Buhrii, Ivan Franko National University of Lviv
    Doctor of Science in Physics and Mathematics, Professor, Department of Mathematical Statistics and Differential Equations, Ivan Franko National University of Lviv, 1 Universytetska Str., Lviv 79000, Ukraine
  • Dariia Yatseniak, Ivan Franko National University of Lviv
    Postgraduate student, Department of Mathematical Statistics and Differential Equations, Ivan Franko National University of Lviv, 1 Universytetska Str., Lviv 79000, Ukraine

References

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Published

2026-05-27

Issue

Vol. 3 No. 1 (2026)

Section

ARTICLES

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Copyright (c) 2026 Олег Бугрій, Дарія Яценяк

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Semilinear parabolic equations on graphs. (2026). Mathematics, Informatics, Physics: Science and Education, 3(1), 22–40. https://doi.org/10.31652/3041-1955-2026-03-01-03