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On the semigroup approach to the interval-valued differential evolution equations

  • Nguyen Thi Kim Son
  • Hoang Viet LongEmail author
Article
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Abstract

In this paper, we introduce the semigroups of semilinear mappings on the space of nonempty compact intervals of \({\mathbb {R}}\). Some important properties of strongly continuous semigroups of interval-valued mappings are investigated. Depending on the different types of generalized Hukuhara differences, the interval-valued infinitesimal generators and resolvent operators are defined and the Hille–Yosida like representation of resolvent operators is given. As an application, the unique existence of mild solutions for Cauchy problems of interval-valued evolution equations is given.

Keywords

Semigroups of interval-valued mappings Infinitesimal generators Resolvent operators Semilinear metric spaces Generalized Hukuhara differentiability Interval-valued evolution equations 

Mathematics Subject Classification

28B10 58C06 54C60 

Notes

Acknowledgements

This paper is supported by NAFOSTED - Vietnam under Grant Contract 101.02-2018.311.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Division of Computational Mathematics and Engineering, Institute for Computational ScienceTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Faculty of Information TechnologyPeople’s Police University of Technology and LogisticsBac NinhVietnam

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