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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Chen, De-Han¹  Hofmann, Bernd³  Zou, Jun² 

[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

关键词: Ill-posed backward evolution equations;    Sectorial operators;    Half-strip operators;    Regularizing family;    Convergence rates of regularized solutions;   

DOI  :  10.1016/j.jde.2018.05.011

来源: Elsevier

【 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.

【 授权许可】

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