ISSIQLIK TARQALISH TENGLAMASI UCHUN TESKARI MASALALAR

Аннотация

This article focuses on inverse problems related to the heat conduction equation. The main objective is to determine the initial temperature distribution based on temperature measurements taken at specific points in time and space. Using the example of the second boundary value problem for the heat equation, the mathematical formulation and characteristics of this inverse problem are examined. The study also discusses approaches for obtaining stable solutions when data is incomplete or noisy. Such inverse problems are crucial in practical applications such as temperature control, studying thermal properties of materials, and optimizing industrial processes. Keywords: Heat conduction equation, inverse problem, direct problem, initial condition, boundary conditions, temperature distribution, stabilization, uncertainty, mathematical modeling, regularization, parameter reconstruction.