Discontinuous differential equation for modelling the Antarctic Circumpolar Current
In this paper, we were concerned with the existence of the solution related to the discontinuous differential equation, which corresponded to the stratification phenomenon in the Antarctic Circumpolar Current (ACC). By considering the piecewise vorticity function, we demonstrated the existence of so...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2024036 |
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| author | Michal Fečkan Shan Li JinRong Wang |
| author_facet | Michal Fečkan Shan Li JinRong Wang |
| author_sort | Michal Fečkan |
| collection | DOAJ |
| description | In this paper, we were concerned with the existence of the solution related to the discontinuous differential equation, which corresponded to the stratification phenomenon in the Antarctic Circumpolar Current (ACC). By considering the piecewise vorticity function, we demonstrated the existence of solution corresponding to the discontinuous differential equation using Green's function, fixed point theory, and topological degree theory. This primarily included cases with piecewise constant vorticity, piecewise linear vorticity, and piecewise nonlinear vorticity. Additionally, we provided some examples to verify our results. |
| format | Article |
| id | doaj-art-057ffdc963f04dc189f3bc294fa02403 |
| institution | Kabale University |
| issn | 2836-3310 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj-art-057ffdc963f04dc189f3bc294fa024032025-01-23T07:55:55ZengAIMS PressCommunications in Analysis and Mechanics2836-33102024-11-0116483685710.3934/cam.2024036Discontinuous differential equation for modelling the Antarctic Circumpolar CurrentMichal Fečkan0Shan Li1JinRong Wang2Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia, and Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49,814 73 Bratislava, SlovakiaDepartment of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China and Supercomputing Algorithm and Application Laboratory of Guizhou University and Gui'an Scientific Innovation Company, Guizhou University, Guiyang, Guizhou 550025, ChinaDepartment of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China and Supercomputing Algorithm and Application Laboratory of Guizhou University and Gui'an Scientific Innovation Company, Guizhou University, Guiyang, Guizhou 550025, ChinaIn this paper, we were concerned with the existence of the solution related to the discontinuous differential equation, which corresponded to the stratification phenomenon in the Antarctic Circumpolar Current (ACC). By considering the piecewise vorticity function, we demonstrated the existence of solution corresponding to the discontinuous differential equation using Green's function, fixed point theory, and topological degree theory. This primarily included cases with piecewise constant vorticity, piecewise linear vorticity, and piecewise nonlinear vorticity. Additionally, we provided some examples to verify our results.https://www.aimspress.com/article/doi/10.3934/cam.2024036antarctic circumpolar currentstratificationgreen's functiondiscontinuous differential equationtopological degree theory |
| spellingShingle | Michal Fečkan Shan Li JinRong Wang Discontinuous differential equation for modelling the Antarctic Circumpolar Current Communications in Analysis and Mechanics antarctic circumpolar current stratification green's function discontinuous differential equation topological degree theory |
| title | Discontinuous differential equation for modelling the Antarctic Circumpolar Current |
| title_full | Discontinuous differential equation for modelling the Antarctic Circumpolar Current |
| title_fullStr | Discontinuous differential equation for modelling the Antarctic Circumpolar Current |
| title_full_unstemmed | Discontinuous differential equation for modelling the Antarctic Circumpolar Current |
| title_short | Discontinuous differential equation for modelling the Antarctic Circumpolar Current |
| title_sort | discontinuous differential equation for modelling the antarctic circumpolar current |
| topic | antarctic circumpolar current stratification green's function discontinuous differential equation topological degree theory |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2024036 |
| work_keys_str_mv | AT michalfeckan discontinuousdifferentialequationformodellingtheantarcticcircumpolarcurrent AT shanli discontinuousdifferentialequationformodellingtheantarcticcircumpolarcurrent AT jinrongwang discontinuousdifferentialequationformodellingtheantarcticcircumpolarcurrent |