In this paper, the Cauchy problem with boundary conditions for an inhomogeneous parabolic equation with changing time direction is investigated. To construct the solution, the method of separation of variables (Fourier method) is employed, leading to a spectral problem where the eigenvalues and eigenfunctions are determined. An a priori estimate for the solution is obtained, theorems of uniqueness and conditional stability in the correctness set are proved. A regularized solution corresponding to the approximate initial data is constructed. The regularization parameter is chosen based on the efficiency estimate derived from the norm of the difference between the exact and the regularized solutions. Numerical experiments were performed for several cases of given data, and the results are presented in tables and graphs. The results show that the regularized solution corresponding to the approximate data closely regularized solution for the exact data, confirming the robustness of the method to errors in the input data.
| Mualliflar | Khajiev, I.O., Shobdarov, E.B., Хажиев, И.О., Шобдаров, Э.Б. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2026-01-11 |
| Son | 6 |
| Betlar | 74-87 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.6_70.2025.06 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.6_70.2025.06 · Maqolaning asl sahifasi
parabolic equation with changing time direction, ill-posed problem, priori estimate, uniqueness, conditionally stability, Lagrange multiplier method, regularization, approximate solution, параболическое уравнение с меняющимся направлением времени, некорректная задача, априорная оценка, единственность, условная устойчивость, метод множителей Лагранжа, регуляризация, приближенное решение
| APA | Khajiev, I.O., Shobdarov, E.B., Хажиев, И.О., & Шобдаров, Э.Б. (2026). Regularization of the Initial-Boundary Value Problem for a Inhomogeneous Parabolic Equation with Changing Time Direction. Ҳисоблаш ва амалий математика муаммолари, (6), 74-87. https://doi.org/10.71310/pcam.6_70.2025.06 |
|---|---|
| GOST (OAK) | Khajiev, I.O. va b. Regularization of the Initial-Boundary Value Problem for a Inhomogeneous Parabolic Equation with Changing Time Direction // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 6. – P. 74-87. – DOI: 10.71310/pcam.6_70.2025.06. |
| MLA | Khajiev, I.O., Shobdarov, E.B., Хажиев, И.О., and Шобдаров, Э.Б. “Regularization of the Initial-Boundary Value Problem for a Inhomogeneous Parabolic Equation with Changing Time Direction.” Ҳисоблаш ва амалий математика муаммолари, (6), 74-87, 2026. https://doi.org/10.71310/pcam.6_70.2025.06 |
| Chicago | Khajiev, I.O., Shobdarov, E.B., Хажиев, И.О., and Шобдаров, Э.Б. “Regularization of the Initial-Boundary Value Problem for a Inhomogeneous Parabolic Equation with Changing Time Direction.” Ҳисоблаш ва амалий математика муаммолари, (6), 74-87 (2026). https://doi.org/10.71310/pcam.6_70.2025.06 |
| Harvard | Khajiev, I.O., Shobdarov, E.B., Хажиев, И.О., and Шобдаров, Э.Б (2026) ‘Regularization of the Initial-Boundary Value Problem for a Inhomogeneous Parabolic Equation with Changing Time Direction’, Ҳисоблаш ва амалий математика муаммолари, (6), 74-87. https://doi.org/10.71310/pcam.6_70.2025.06 |
| BibTeX | @article{khajievio2026,
title = {Regularization of the Initial-Boundary Value Problem for a Inhomogeneous Parabolic Equation with Changing Time Direction},
author = {Khajiev, I.O. and Shobdarov, E.B. and Хажиев, И.О. and Шобдаров, Э.Б.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2026},
number = {6},
pages = {74-87},
doi = {10.71310/pcam.6_70.2025.06},
url = {https://doi.org/10.71310/pcam.6_70.2025.06}
} |
Boshqa maqola uchun iqtibos tayyorlash
This article describes and provides examples of the FrOsFHN software package for the quantitative and qualitative analysis of a nonlinear FitzHugh-Nagumo oscillator with variable memory (the fractional FitzHugh-Nagumo…
This paper presents the design and analysis of an innovative solar-powered water supply system for multi-storey residential buildings under conditions of high solar insolation and limited energy resources. Instead of…
The article analyzes the hydrodynamic processes associated with underground mining, in particular, the acid extraction of precious metals from ore deposits. In order to comprehensively study, monitor and predict the…
This article proposes a dynamic model of a coupled thermoelasticity problem under stress. A coupled boundary value problem is formulated, consisting of three differen tial equations for the stress and temperature tensor…
The paper models the spatiotemporal dynamics of the Kattakurgan Reservoir area using satellite-based water and vegetation indices combined with ensemble machinelearning methods. Multi-year time series of NDWI, NDVI, and…
This paper proposes a Context-adaptive Audio-Visual Neural Network (CAVN) model for anomaly detection in public safety systems. Existing approaches primarily rely on visual data and employ simple fusion strategies for…
For the first time, a fractal solar collector operating in the cogeneration mode is proposed. In this context, we are talking about a modern innovative system that uses fractal structures to optimize the processes of…
The paper addresses a numerical solution of a plane–radial boundary inverse problem for the relaxation filtration equation describing fluid flow in an elastically deformable porous medium. The study is motivated by the…
Hypersingular integral equations are encountered in a number of fields, such as the dynamics of air and fluid flow, elasticity, and wave propagation theory. Analytical solutions for these integral equations exist, but…
Integrals of rapidly oscillating functions arise mainly in the theory of special functions and Fourier analysis, but also in other applied and computational sciences and engineering, for example, in theoretical physics…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2026-yil arxivi
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.