Mathematical Foundations Of Inverse And Ill-Posed Problems

Abstract

This article examines the fundamental concepts of inverse and ill-posed problems, their classification, and theoretical foundations in the context of mathematical physics. Issues related to the formulation of inverse problems based on differential equations and boundary conditions are discussed, including the correctness and stability of their solutions. The differences between weakly and strongly ill-posed problems are also analyzed, along with their practical applications and methods for stabilizing solutions.