Continuous regularization of nonlinear ill-posed problems

TL;DR

This paper introduces a general continuous regularization method for nonlinear ill-posed problems, demonstrating convergence to solutions and providing application examples and theoretical proofs.

Contribution

It develops a novel continuous regularization approach for nonlinear ill-posed problems with proven convergence and practical application examples.

Findings

Convergence theorems established for the regularization method

Method successfully approximates solutions of nonlinear ill-posed problems

Applications demonstrate effectiveness of the approach

Abstract

A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the original nonlinear stationary problem. Examples of applications of the general method are given. Convergence theorems are proved.