Existence of a Generalized Solution for the Fractional Contact Problem
In this paper, we take into consideration the mathematical analysis of time-dependent quasistatic processes involving the contact between a solid body and an extremely rigid structure, referred to as a foundation. It is assumed that the constitutive law is fractional long-memory viscoelastic. The co...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/8316373 |
| _version_ | 1811175576839389184 |
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| author | Leila Ait kaki Nouria Arar Mohammed S. Abdo M. Daher Albalwi |
| author_facet | Leila Ait kaki Nouria Arar Mohammed S. Abdo M. Daher Albalwi |
| author_sort | Leila Ait kaki |
| collection | DOAJ |
| description | In this paper, we take into consideration the mathematical analysis of time-dependent quasistatic processes involving the contact between a solid body and an extremely rigid structure, referred to as a foundation. It is assumed that the constitutive law is fractional long-memory viscoelastic. The contact is considered to be bilateral and is modeled around Tresca’s law. We establish the existence of the generalized solution’s result. The proof is supported by the surjectivity of the multivalued maximum monotone operator, Rothe’s semidiscretization method, and arguments for evolutionary variational inequality. |
| first_indexed | 2024-04-10T19:39:05Z |
| format | Article |
| id | doaj.art-b7a77038cf144ee486cc411e7d70538c |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-04-10T19:39:05Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-b7a77038cf144ee486cc411e7d70538c2023-01-30T00:11:05ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/8316373Existence of a Generalized Solution for the Fractional Contact ProblemLeila Ait kaki0Nouria Arar1Mohammed S. Abdo2M. Daher Albalwi3Applied Mathematics and Didactic LaboratoryMathematics and Decision Sciences LaboratoryDepartment of MathematicsYanbu Industrial CollegeIn this paper, we take into consideration the mathematical analysis of time-dependent quasistatic processes involving the contact between a solid body and an extremely rigid structure, referred to as a foundation. It is assumed that the constitutive law is fractional long-memory viscoelastic. The contact is considered to be bilateral and is modeled around Tresca’s law. We establish the existence of the generalized solution’s result. The proof is supported by the surjectivity of the multivalued maximum monotone operator, Rothe’s semidiscretization method, and arguments for evolutionary variational inequality.http://dx.doi.org/10.1155/2023/8316373 |
| spellingShingle | Leila Ait kaki Nouria Arar Mohammed S. Abdo M. Daher Albalwi Existence of a Generalized Solution for the Fractional Contact Problem Journal of Mathematics |
| title | Existence of a Generalized Solution for the Fractional Contact Problem |
| title_full | Existence of a Generalized Solution for the Fractional Contact Problem |
| title_fullStr | Existence of a Generalized Solution for the Fractional Contact Problem |
| title_full_unstemmed | Existence of a Generalized Solution for the Fractional Contact Problem |
| title_short | Existence of a Generalized Solution for the Fractional Contact Problem |
| title_sort | existence of a generalized solution for the fractional contact problem |
| url | http://dx.doi.org/10.1155/2023/8316373 |
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