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|Title:||Exponential dichotomies and Fredholm operator for parabolic equations||Authors:||Kwek, K.-H.
|Issue Date:||16-May-2002||Citation:||Kwek, K.-H., Zhang, W. (2002-05-16). Exponential dichotomies and Fredholm operator for parabolic equations. Mathematical and Computer Modelling 35 (11-12) : 1245-1259. ScholarBank@NUS Repository. https://doi.org/10.1016/S0895-7177(02)00083-3||Abstract:||It proved true for infinite-dimensional systems that the operator F:= d/dt - A(t) is Fredholm when A(t), roughly speaking, admits exponential dichotomies on both R+ and R-. It is also interesting to study its converse problem. Although in [1,2] results were given to the question when the Fredholm alternative for bounded solutions of parabolic equations implies exponential dichotomies, but neither of them gave a direct answer to the operator F. In this paper, we try to obtain a direct answer for parabolic equations defined on a Banach space and to give an approach in the space of functions of compact support. © 2002 Elsevier Science Ltd. All rights reserved.||Source Title:||Mathematical and Computer Modelling||URI:||http://scholarbank.nus.edu.sg/handle/10635/112989||ISSN:||08957177||DOI:||10.1016/S0895-7177(02)00083-3|
|Appears in Collections:||Staff Publications|
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