Linear ill-posed problems and dynamical systems
数学物理
2007-05-23 v4 偏微分方程分析
动力系统
泛函分析
math.MP
摘要
A linear equation Au=f (1) with a bounded, injective, but not boundedly invertible linear operator in a Hilbert space H is studied. A new approach to solving linear ill-posed problems is proposed. The approach consists of solving a Cauchy problem for a linear equation in H, which is a dynamical system, proving the existence and uniqueness of its global solution u(t), and establishing that u(t) tends to a limit y, as t tends to infinity, and this limit y solves equation (1). The case when f in (1) is given with some error is also studied.
引用
@article{arxiv.math-ph/0008011,
title = {Linear ill-posed problems and dynamical systems},
author = {Alexander G. Ramm},
journal= {arXiv preprint arXiv:math-ph/0008011},
year = {2007}
}