Article

Initial-boundary value problem for an inhomogeneous heat equation with piecewise constant delay

D. K. DurdievV.I. Romanovsky Institute of Mathematics of the Academy of Sciences of Uzbekistan; Bukhara State UniversityS. H. XolikovNavoi State Pedagogical InstituteH. H. TurdievBukhara State University

Izvestiya Vysshikh Uchebnykh Zavedenii Matematikajournal2026

ABI

Abstract

In this paper, an initial-boundary value problem for an inhomogeneous heat equation with a piecewise constant argument and Dirichlet boundary conditions is considered. The Fourier method is used to investigate the problem. By expanding the solution in terms of eigenfunctions, the initial-boundary value problem is reduced to the Cauchy problem for an ordinary differential equation with respect to the expansion coefficients with a piecewise continuous argument. The existence and uniqueness of the solution to this problem are proved. As a result, it is shown that the original problem has a unique solution, which is constructed in explicit form.

Topics

Differential Equations and Boundary Problems Nonlinear Differential Equations Analysis Stability and Controllability of Differential Equations

Identifiers

DOI: 10.26907/0021-3446-2026-3-12-22

Citations and references

Cited by 023 references

Metrics — AkademScholar · Coming soon