Mathematical models of many applied problems lead to the need to solve interiorboundary value problems for partial differential equations. The problem under study belongs to the class of ill-posed problems in mathematical physics. The issue of small denominators arises; the existence and uniqueness of the solution depend on the numerical properties of the problem data. Theorems on the uniqueness of the solution and its conditional stability on the well-posedness set are proven, a priori estimates for the solution are obtained, and approximate solutions are constructed using the regularization method. The development of approximate methods for their solution is based on the construction and analysis of numerical methods for solving problems with interior and boundary data for the basic (fundamental, model) equations of mathematical physics.
| Mualliflar | Fayazov, K.S., Abdullaeva, Z.Sh., Фаязов, К.С., Абдуллаева, З.Ш. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2025-11-16 |
| Son | 5 |
| Betlar | 86-101 |
| Til | Rus |
| DOI | 10.71310/pcam.5_69.2025.07 |
DOI: 10.71310/pcam.5_69.2025.07 · Maqolaning asl sahifasi
ill-posed problem, mixed type, inverse problem, uniqueness, system of equations, некорректная задача, смешанный тип, обратная задача, единственность, система уравнений
In this article, we present a detailed study on the determination of the coefficients of a quadrature formula that involves derivatives, making use of the so-called the phi – function method. This method provides a…
Numerical integration of definite integrals plays a crucial role in both fundamental and applied sciences. The precision of approximate integral calculations depends on the initial data and specific conditions, which…
This paper presents a method of semantic modeling based on representing complex objects and phenomena as informational aggregates composed of core, designating, characterizing, and associative entities. Each entity is…
The game problem of transferring the trajectory of a dynamic system controlled by two players whose goals are opposite, from any point of a given set to a terminal set is considered. The given set is described by the…
This paper formalizes and extends the classic concept of the "Middle Turkic"language (Karimov–Mutalov, 1992) by applying tools from corpus and computational linguistics. The proposed model frames the selection of an…
A mathematical and numerical model is presented for the process of liquid solution filtration in a cylindrical porous filter. The model is based on the Brinkman-Darcy equations, describing fluid motion in a porous…
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 a detailed comparative analysis of the numerical results of the 2D Backward Facing Step (2DBFS) problem. using modern software packages OpenFOAM, COMSOL Multiphysics and Ansys Fluent. The study…
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 paper presents a mathematical model of pollutant dispersion in turbulent airflows within the atmospheric boundary layer. The model is based on the advection–diffusion equation and the system of Navier–Stokes…