Global boundedness and asymptotic behavior of the chemotaxis system for Alopecia Areata with weakly singular sensitivity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918474621648896 |
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| author | Xiang, Pengxue Cao, Yuebo Yang, Hongying |
| author_facet | Xiang, Pengxue Cao, Yuebo Yang, Hongying |
| contents | This paper considers the homogeneous Neumann initial-boundary value problem for Alopecia Areata chemotaxis model with weakly singular sensitivity. For any appropriately regular initial conditions,it is shown that the problem admits a global boundedness of classical solutions in two spatial dimensions. Moreover, through the explicit construction of Lyapunov functions, we establish that the globally bounded solution converges exponentially to a constant steady state. The paper concludes with numerical experiments that serve to visually illustrate and corroborate some of the theoretically derived findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26905 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global boundedness and asymptotic behavior of the chemotaxis system for Alopecia Areata with weakly singular sensitivity Xiang, Pengxue Cao, Yuebo Yang, Hongying Analysis of PDEs This paper considers the homogeneous Neumann initial-boundary value problem for Alopecia Areata chemotaxis model with weakly singular sensitivity. For any appropriately regular initial conditions,it is shown that the problem admits a global boundedness of classical solutions in two spatial dimensions. Moreover, through the explicit construction of Lyapunov functions, we establish that the globally bounded solution converges exponentially to a constant steady state. The paper concludes with numerical experiments that serve to visually illustrate and corroborate some of the theoretically derived findings. |
| title | Global boundedness and asymptotic behavior of the chemotaxis system for Alopecia Areata with weakly singular sensitivity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.26905 |