- PII
- 10.31857/S0374064125010037-1
- DOI
- 10.31857/S0374064125010037
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 61 / Issue number 1
- Pages
- 22-34
- Abstract
- In this paper the boundary value problem (BVP) for diffusion equation with piecewise constant arguments is studied. By using the separation of variables method, the considered BVP is reduced to the investigation of the existence conditions of solutions of initial value problems for differential equation with piecewise constant arguments. Existence conditions of infinitely many solutions or emptiness for considered differential equation are established and explicit formula for these solutions are obtained. Several examples are given to illustrate the obtained results.
- Keywords
- уравнение диффузии кусочно-постоянный аргумент периодическое решение
- Date of publication
- 19.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 9
References
- 1. Hale, J.K. Introduction to Functional Differential Equations / J.K. Hale, S.M.V. Lunel. — New York : Springer Science Business Media, 2013. — 449 p.
- 2. Almost Periodic Solutions of Differential Equations in Banach Spaces / Y. Hino, T. Naito, N.V. Minh, J.S. Shin. — London ; New York : Taylor & Francis, 2002. — 249 p.
- 3. Wiener, J. Generalized Solutions of Functional Differential Equations / J. Wiener. — Singapore ; New Jersey ; London ; Hong Kong : World Scientific, 1993. — 410 p.
- 4. Cooke, K.L. A survey of differential equations with piecewise continuous arguments / K.L. Cooke, J. Wiener // Delay Differential Equations and Dynamical Systems, Proc. of a Conf. in Honor of Kenneth Cooke Held in Claremont, California / Eds. S. Busenberg, M. Martelli. — Berlin : Springer-Verlag, 1991. — P. 1–15.
- 5. Muminov, M.I. On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments / M.I. Muminov // Advances in Difference Equations. — 2017. — V. 336. — P. 1–17.
- 6. Muminov, M.I. Existence conditions for periodic solutions of second-order neutral delay differential equations with piecewise constant arguments / M.I. Muminov, Ali H.M. Murid // Open Math. — 2020. — V. 18, № 1. — P. 93–105.
- 7. Wiener, J. Boundary-value problems for partial differential equations with piecewise constant delay / J. Wiener // Int. J. Math. Math. Sci. — 1991. — V. 14. — P. 301–321.
- 8. Wiener, J. Partial differential equations with piecewise constant delay / J. Wiener, L. Debnath // Int. J. Math. Math. Sci. — 1991. — V. 14. — P. 485–496.
- 9. Wiener, J. Oscillatory and periodic solutions to a diffusion equation of neutral type / J. Wiener, W. Heller // Int. J. Math. Math. Sci. — 1999. — V. 22, № 2. — P. 313–348.
- 10. Wiener, J. Boundary value problems for the diffusion equation with piecewise continuous time delay / J. Wiener, L. Debnath // Int. J. Math. Math. Sci. — 1997. — Т. 20, № 1. — С. 187–195.
- 11. Buyukkahraman, M.L. On a partial differential equation with piecewise constant mixed arguments / M.L. Buyukkahraman, H. Bereketoglu // Iran J. Sci. Technol. Trans. Sci. — 2020. — V. 44. — P. 1791–1801.
- 12. Veloz, T. Existence, computability and stability for solutions of the diffusion equation with general piecewise constant argument / T. Veloz, M. Pinto // J. Math. Anal. Appl. — 2015. — V. 426, № 1. — P. 330–339.
- 13. Wang, Q. Analytical and numerical stability of partial differential equations with piecewise constant arguments / Q. Wang, J. Wen // Numer. Methods Partial Differ. Equat. — 2014. — V. 30, № 1. — P. 1–16.
- 14. Muminov, M.I. Forced diffusion equation with piecewise continuous time delay / M.I. Muminov, T.A. Radjabov // Adv. Math. Sci. J. — 2021. — V. 10, № 4. — P. 2269–2283.
- 15. Muminov, M.I. On existence conditions for periodic solutions to a differential equation with constant argument / M.I. Muminov, T.A. Radjabov // Nanosystems: Phys. Chem. Math. — 2022. — V. 13, № 5. — P. 491–497.
- 16. Muminov, M.I. Existence conditions for 2-periodic solutions to a non-homogeneous differential equations with piecewise constant argument / M.I. Muminov, T.A. Radjabov // Examples and Counterexamples. — 2024. — V. 5. — Art. 100145.
