THE INVERSE PROBLEM OF DETERMINING THE TIME-DEPENDENT COEFFICIENT IN THE HEAT CONDUCTION EQUATION

Abstract

 This article investigates the inverse problem of determining a time-dependent coefficient in the heat conduction equation. The study focuses on both theoretical and practical aspects of identifying unknown parameters in mathematical models describing heat transfer processes. The heat conduction equation is one of the fundamental equations of mathematical physics and plays an important role in modeling thermal processes in various fields of science and engineering. In this work, the formulation of inverse problems related to the identification of time-dependent coefficients is analyzed, and the conditions of well-posedness, stability, and uniqueness of the solution are discussed. Special attention is given to different mathematical approaches used to solve such problems, including integral equation methods, variational techniques, and analytical methods. Furthermore, the paper highlights the importance of solving inverse problems for accurate modeling of thermal processes, engineering systems, and technological applications.