Journal article
A new class of fractional differential hemivariational inequalities with application to an incompressible Navier-Stokes system coupled with a fractional diffusion equation
Izvestii͡a︡ Akademii nauk. Serii͡a︡ matematicheskai͡a, Vol.87(2), pp.133-167
2023
DOI: 10.4213/im9251
Abstract
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.
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.
Details
- Title: Subtitle
- A new class of fractional differential hemivariational inequalities with application to an incompressible Navier-Stokes system coupled with a fractional diffusion equation
- Creators
- Shengda Zeng - Jagiellonian UniversityStanislaw Migórski - Jagiellonian UniversityWeimin Han - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Izvestii͡a︡ Akademii nauk. Serii͡a︡ matematicheskai͡a, Vol.87(2), pp.133-167
- DOI
- 10.4213/im9251
- ISSN
- 1607-0046
- eISSN
- 2587-5906
- Grant note
- name: Startup Project of Doctor Scientific Research of Yulin Normal University, award: G2020ZK07; DOI: 10.13039/501100000781, name: European Research Council, award: 823731-CONMECH; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 12001478; DOI: 10.13039/100000893, name: Simons Foundation, award: 850737; DOI: 10.13039/501100002858, name: China Postdoctoral Science Foundation, award: 2022M721560; DOI: 10.13039/501100004281, name: Narodowe Centrum Nauki, award: 2021/41/B/ST1/01636; name: Ministry of Science and Higher Education, Poland, award: 4004/GGPJII/H2020/2018/0, 440328/PnH2/2019; DOI: 10.13039/501100004281, name: Natural Science Foundation of Guangxi Province, award: 2021GXNSFFA196004, 2022AC21071, 2018GXNSFDA138002
- Language
- Russian
- Date published
- 2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984413075702771
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