Article

Existence of Solutions of a Boundary Value Problem fora Diffusion Equation with Piecewise Constant Arguments

M. I. MuminovRomanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, 100170, UzbekistanTirkash A. RadjabovKimyo International University in Tashkent, Tashkent, 100121, Uzbekistan

Differential Equationsjournal2025en

ABI

Abstract

We study a boundary value problem for a diffusion equation with piecewise constant arguments. By separation of variables, the analysis of this boundary value problem is reduced to that of the existence conditions for solutions of initial value problems for a differential equation with piecewise constant arguments. Conditions for the existence of infinitely many solutions or the emptiness of the solution set are established for the differential equation in question, and explicit formulas for these solutions are obtained. Several examples are given to illustrate the results.

Topics

Differential Equations and Numerical Methods Advanced Mathematical Modeling in Engineering Differential Equations and Boundary Problems

Identifiers

DOI: 10.1134/s0012266125010033

Citations and references

Cited by 013 references

Metrics — AkademScholar · Coming soon