Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 265, Issue 8, Pages 3533-3566Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2018.05.011
Keywords
Ill-posed backward evolution equations; Sectorial operators; Half-strip operators; Regularizing family; Convergence rates of regularized solutions
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Funding
- Hong Kong RGC General Research Fund [14322516]
- Direct Grant for Research from The Chinese University of Hong Kong
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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.
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