Regularization and convergence for ill-posed backward evolution equations in Banach spaces

被引：16

作者：

Chen, De-Han ^{[1
]}

Hofmann, Bernd ^{[3
]}

Zou, Jun ^{[2
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[3] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 265卷 / 08期

关键词：

Ill-posed backward evolution equations; Sectorial operators; Half-strip operators; Regularizing family; Convergence rates of regularized solutions; HOLOMORPHIC FUNCTIONAL-CALCULUS; APPROXIMATE SOURCE CONDITIONS; H-INFINITY-CALCULUS; RANGE INCLUSIONS; RECONSTRUCTION; OPERATORS; RATES;

D O I：

10.1016/j.jde.2018.05.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This work is concerned with a mathematical study of ill-posed backward evolution equations associated with densely defined linear differential operators in Banach spaces. A general approach is presented to investigate the convergence and stability of a class of regularized solutions for ill-posed backward evolution equations associated with sectorial or half-strip operators. Generalized concepts of qualification pairs and index functions are introduced to characterize the explicit convergence rates of the concerned regularized solutions. Applications of our results to general backward evolution equations are also investigated. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：3533 / 3566

页数：34

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