Mathematics, Informatics, Physics: Science and Education

Electronic scientific journal

Vol. 3 No. 1 (2026)
ARTICLES

Semilinear parabolic equations on graphs

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  • Oleh Buhrii,
  • Dariia Yatseniak
Oleh Buhrii
Ivan Franko National University of Lviv
Bio
Dariia Yatseniak
Ivan Franko National University of Lviv
Bio

Published 2026-05-27

Keywords

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

Copyright (c) 2026 Олег Бугрій, Дарія Яценяк

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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
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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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