1. bookVolume 114 (2017): Issue 9 (September 2017)
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eISSN
2353-737X
First Published
20 May 2020
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1 time per year
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Open Access

Continuous dependence of mild solutions, on initial nonlocal data, of the nonlocal semilinear evolution cauchy problems

Published Online: 29 May 2020
Volume & Issue: Volume 114 (2017) - Issue 9 (September 2017)
Page range: 151 - 158
Journal Details
License
Format
Journal
eISSN
2353-737X
First Published
20 May 2020
Publication timeframe
1 time per year
Languages
English
Abstract

The aim of the paper is to prove two theorems on continuous dependence of mild solutions, on initial nonlocal data, of the nonlocal semilinear evolution Cauchy problems. For this purpose, the method of semigroups and the theory of cosine family in Banach spaces are applied. The paper is based on publications [1–6] and is a generalization of paper [3].

Keywords

[1] Byszewski L., Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, Selected Problems of Mathematics, Cracow University of Technology, Anniversary Issue 6, 1995, 25–33.Search in Google Scholar

[2] Byszewski L., Winiarska T., An abstract nonlocal second order evolution problem, Opuscula Mathematica 32.1, 2012, 75–82.10.7494/OpMath.2012.32.1.75Search in Google Scholar

[3] Byszewski L., Winiarska T., Continuous dependence of mild solutions, on initial nonlocal data, of the nonlocal evolution Cauchy problems, Technical Transactions, 1-NP/2013, 27–32.Search in Google Scholar

[4] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1983.10.1007/978-1-4612-5561-1Search in Google Scholar

[5] Szarski J., Differential Inequalities, Polish Scientific Publishers, Warszawa 1967.Search in Google Scholar

[6] Winiarska T., Differential Equations with Parameters, Monograph 68, Cracow University of Technology, Kraków 1988.Search in Google Scholar

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