On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian Operator
Several cells and microorganisms, such as bacteria and somatic, have many essential features, one of which can be modeled by the chemotaxis system, which we consider to be our main interest in this article. More precisely, we studied the hyperbolic system derived from the chemotaxis model with fract...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/1140032 |
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| _version_ | 1850177071874048000 |
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| author | Oussama Melkemi Mohammed S. Abdo M.A. Aiyashi M. Daher Albalwi |
| author_facet | Oussama Melkemi Mohammed S. Abdo M.A. Aiyashi M. Daher Albalwi |
| author_sort | Oussama Melkemi |
| collection | DOAJ |
| description | Several cells and microorganisms, such as bacteria and somatic, have many essential features, one of which can be modeled by the chemotaxis system, which we consider to be our main interest in this article. More precisely, we studied the hyperbolic system derived from the chemotaxis model with fractional dissipation, which is a generalization for the hyperbolic system with classical dissipation. The results of this article are divided into two parts. In the first part, we used energy methods to obtain the existence of small solutions in the Besov spaces. The second one deals with the optimal decay of perturbed solutions using a refined time-weighted energy combined with the Littlewood-Paley decomposition technique. To the authors’ best knowledge, this type of system (with fractional dissipation) has not been studied in the literature. |
| format | Article |
| id | doaj-art-aebc01414be541bf86f282eae0370bc1 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-aebc01414be541bf86f282eae0370bc12025-08-20T02:19:06ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/1140032On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian OperatorOussama Melkemi0Mohammed S. Abdo1M.A. Aiyashi2M. Daher Albalwi3Laboratory of Partial Differential Equations and ApplicationsDepartment of MathematicsDepartment of MathematicsYanbu Industrial CollegeSeveral cells and microorganisms, such as bacteria and somatic, have many essential features, one of which can be modeled by the chemotaxis system, which we consider to be our main interest in this article. More precisely, we studied the hyperbolic system derived from the chemotaxis model with fractional dissipation, which is a generalization for the hyperbolic system with classical dissipation. The results of this article are divided into two parts. In the first part, we used energy methods to obtain the existence of small solutions in the Besov spaces. The second one deals with the optimal decay of perturbed solutions using a refined time-weighted energy combined with the Littlewood-Paley decomposition technique. To the authors’ best knowledge, this type of system (with fractional dissipation) has not been studied in the literature.http://dx.doi.org/10.1155/2023/1140032 |
| spellingShingle | Oussama Melkemi Mohammed S. Abdo M.A. Aiyashi M. Daher Albalwi On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian Operator Journal of Mathematics |
| title | On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian Operator |
| title_full | On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian Operator |
| title_fullStr | On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian Operator |
| title_full_unstemmed | On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian Operator |
| title_short | On the Global Well-Posedness for a Hyperbolic Model Arising from Chemotaxis Model with Fractional Laplacian Operator |
| title_sort | on the global well posedness for a hyperbolic model arising from chemotaxis model with fractional laplacian operator |
| url | http://dx.doi.org/10.1155/2023/1140032 |
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