THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONS

The purpose of the article is to reveal the problems in solving inverse and ill-posed problems with given differential equations. When studying any physical phenomenon, the researcher first of all creates its mathematical idealization or, in other words, a mathematical model, that is, neglecting the secondary characteristics of the phenomenon, he writes down the basic laws governing this phenomenon in mathematical form. Very often these laws can be expressed in the form of differential equations. The authors emphasize the main features and fundamental concepts of correct and incorrect problems of mathematical physics. In addition, a review and classification of inverse problems of mathematical physics is presented. A number of examples of correct and incorrect problems are given. A review of methods for solving such problems is given.