A new class of fractional differential hemivariational inequalities with application to an incompressible Navier–Stokes system coupled with a fractional diffusion equation
- Авторы: Zeng S.1,2, Migórski S.3,4, Han W.5
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Учреждения:
- Yulin Normal University
- Nanjing University
- Beibu Gulf University
- Jagiellonian University
- University of Iowa
- Выпуск: Том 87, № 2 (2023)
- Страницы: 133-167
- Раздел: Статьи
- URL: https://journals.rcsi.science/1607-0046/article/view/133906
- DOI: https://doi.org/10.4213/im9251
- ID: 133906
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Аннотация
This paper is devoted to the study of a new and complicated dynamical system, called a fractional differential hemivariational inequality, which consists of a quasilinear evolution equation involving the fractional Caputo derivative operator and a coupled generalized parabolic hemivariational inequality. Under certain general assumptions, existence and regularity of a mild solution to the dynamical system are established by employing a surjectivity result for weakly–weakly upper semicontinuous multivalued mappings, and a feedback iterative technique together with a temporally semi-discrete approach through the backward Euler difference scheme with quasi-uniform time-steps. To illustrate the applicability of the abstract results, we consider a nonstationary and incompressible Navier–Stokes system supplemented by a fractional reaction–diffusion equation, which is studied as a fractional hemivariational inequality. Bibliography: 57 titles.
Об авторах
Shengda Zeng
Yulin Normal University; Nanjing University
Email: zengshengda@163.com
Stanisław Migórski
Beibu Gulf University; Jagiellonian University
Email: stanislaw.migorski@uj.edu.pl
доктор наук, профессор
Weimin Han
University of Iowa
Email: weimin-han@uiowa.edu
доктор физико-математических наук, профессор
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