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

Byszewski, Ludwik

doi:10.4467/2353737XCT.17.155.7167

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

Technical Transactions

Volume 114 (2017): Issue 9 (September 2017)

By: Ludwik Byszewski

Open Access

|May 2020

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].

References

[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.
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[2] Byszewski L., Winiarska T., An abstract nonlocal second order evolution problem, Opuscula Mathematica 32.1, 2012, 75–82.10.7494/OpMath.2012.32.1.75
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[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.
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[4] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1983.10.1007/978-1-4612-5561-1
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[5] Szarski J., Differential Inequalities, Polish Scientific Publishers, Warszawa 1967.
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[6] Winiarska T., Differential Equations with Parameters, Monograph 68, Cracow University of Technology, Kraków 1988.
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DOI: https://doi.org/10.4467/2353737XCT.17.155.7167 | Journal eISSN: 2353-737X | Journal ISSN: 0011-4561

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Language: English

Page range: 151 - 158

Published on: May 29, 2020

Published by: Cracow University of Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

semilinear evolution Cauchy problems,

continuous dependence of solutions,

nonlocal conditions

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© 2020 Ludwik Byszewski, published by Cracow University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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