History of ill-posed problems and their application to solve various mathematical problems
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Abstract
This study aims to provide an understanding of well-posed and incorrectly-posed problems, as well as the developed methods for solving incorrectly-posed applied problems in mathematics. The history and significance of incorrectly-posed problems in solving various applied problems in the natural sciences are explored in detail. The study of methods for solving ill-posed problems has garnered significant interest among researchers, who are actively conducting research in this field. The theory of incorrectly-posed problems is a rapidly developing area in mathematical physics and natural sciences.In the practical realm, most problems are ill-posed, requiring decision-making under conditions of uncertainty, overdetermination, or inconsistency. The main conclusion drawn from this study is that solving incorrectly-posed problems cannot be accomplished solely by learning from well-posed problems.
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