Continuous regularization of nonlinear ill-posed problems

R. Airapetyan; A. G. Ramm; A. Smirnova

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Continuous regularization of nonlinear ill-posed problems

R. Airapetyan·A. G. Ramm·A. Smirnova

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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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R. Airapetyan, A. G. Ramm, A. Smirnova. 1999-11-27. Continuous regularization of nonlinear ill-posed problems. https://arxiv.org/abs/math-ph/9911041

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