Continuous regularization of nonlinear ill-posed problems

Ruben Hayrapetyan; Alexander G. Ramm; A. Smirnova

Continuous regularization of nonlinear ill-posed problems

Ruben Hayrapetyan
, Alexander G. Ramm
, A. Smirnova

Kettering University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	arXiv
State	Published - Dec 27 1999

Disciplines

Mechanical Engineering

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Cite this

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title = "Continuous regularization of nonlinear ill-posed problems",

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. ",

author = "Ruben Hayrapetyan and Ramm, \{Alexander G.\} and A. Smirnova",

year = "1999",

month = dec,

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language = "American English",

journal = "arXiv",

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T1 - Continuous regularization of nonlinear ill-posed problems

AU - Hayrapetyan, Ruben

AU - Ramm, Alexander G.

AU - Smirnova, A.

PY - 1999/12/27

Y1 - 1999/12/27

N2 - 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.

AB - 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.

M3 - Article

JO - arXiv

JF - arXiv

ER -