Continuous regularization of nonlinear ill-posed problems

1999/11/27 by Ruben G. Airapetyan, А. Г. Рамм, Airapetyan, R. +3
Engineering · Mathematics · #47H05 #58C15 #65J15 #65M30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Heat Transfer and Mathematical Modeling #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.math-ph/9911041

openalex publication_date 1999/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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