A finite element approach to the Keller–Segel Chemotaxis system with impact of nonlocal diffusion
Abstract This paper presents the investigation of a boundedness solution for a Keller–Segel chemotaxis (KSC) system with nonlocal diffusion. In order to achieve boundedness, we derive the necessary and sufficient condition based on the assumption of ensuring a unique classical global bounded solutio...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-024-01976-7 |
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| author | A. Baskar V. Parthiban |
| author_facet | A. Baskar V. Parthiban |
| author_sort | A. Baskar |
| collection | DOAJ |
| description | Abstract This paper presents the investigation of a boundedness solution for a Keller–Segel chemotaxis (KSC) system with nonlocal diffusion. In order to achieve boundedness, we derive the necessary and sufficient condition based on the assumption of ensuring a unique classical global bounded solution for the proposed KSC system. In this work, the proposed system’s boundedness condition is determined based on three particular situations: when χ < χ ∗ $\chi <\chi ^{*}$ , χ < κ $\chi <\kappa $ , and when χ = κ $\chi =\kappa $ . Finally, the effectiveness of the nonlinear and nonlocal diffusion terms in the KSC system is demonstrated through numerical simulations under consideration of the values of system parameters. From the simulation results, we can confirm the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-9c5f7cc1b1044cbea0945844ddebbc44 |
| institution | OA Journals |
| issn | 1687-2770 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-9c5f7cc1b1044cbea0945844ddebbc442025-08-20T02:31:55ZengSpringerOpenBoundary Value Problems1687-27702024-12-012024112010.1186/s13661-024-01976-7A finite element approach to the Keller–Segel Chemotaxis system with impact of nonlocal diffusionA. Baskar0V. Parthiban1Department of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyAbstract This paper presents the investigation of a boundedness solution for a Keller–Segel chemotaxis (KSC) system with nonlocal diffusion. In order to achieve boundedness, we derive the necessary and sufficient condition based on the assumption of ensuring a unique classical global bounded solution for the proposed KSC system. In this work, the proposed system’s boundedness condition is determined based on three particular situations: when χ < χ ∗ $\chi <\chi ^{*}$ , χ < κ $\chi <\kappa $ , and when χ = κ $\chi =\kappa $ . Finally, the effectiveness of the nonlinear and nonlocal diffusion terms in the KSC system is demonstrated through numerical simulations under consideration of the values of system parameters. From the simulation results, we can confirm the effectiveness of the proposed method.https://doi.org/10.1186/s13661-024-01976-7BoundednessChemotaxisGlobal existenceNumerical simulation |
| spellingShingle | A. Baskar V. Parthiban A finite element approach to the Keller–Segel Chemotaxis system with impact of nonlocal diffusion Boundary Value Problems Boundedness Chemotaxis Global existence Numerical simulation |
| title | A finite element approach to the Keller–Segel Chemotaxis system with impact of nonlocal diffusion |
| title_full | A finite element approach to the Keller–Segel Chemotaxis system with impact of nonlocal diffusion |
| title_fullStr | A finite element approach to the Keller–Segel Chemotaxis system with impact of nonlocal diffusion |
| title_full_unstemmed | A finite element approach to the Keller–Segel Chemotaxis system with impact of nonlocal diffusion |
| title_short | A finite element approach to the Keller–Segel Chemotaxis system with impact of nonlocal diffusion |
| title_sort | finite element approach to the keller segel chemotaxis system with impact of nonlocal diffusion |
| topic | Boundedness Chemotaxis Global existence Numerical simulation |
| url | https://doi.org/10.1186/s13661-024-01976-7 |
| work_keys_str_mv | AT abaskar afiniteelementapproachtothekellersegelchemotaxissystemwithimpactofnonlocaldiffusion AT vparthiban afiniteelementapproachtothekellersegelchemotaxissystemwithimpactofnonlocaldiffusion AT abaskar finiteelementapproachtothekellersegelchemotaxissystemwithimpactofnonlocaldiffusion AT vparthiban finiteelementapproachtothekellersegelchemotaxissystemwithimpactofnonlocaldiffusion |