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arXiv · 2604.26905

Global boundedness and asymptotic behavior of the chemotaxis system for Alopecia Areata with weakly singular sensitivity

Pengxue Xiang·Yuebo Cao·Hongying Yang
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Abstract

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.

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Pengxue Xiang, Yuebo Cao, Hongying Yang. 2026-04-29. Global boundedness and asymptotic behavior of the chemotaxis system for Alopecia Areata with weakly singular sensitivity. https://arxiv.org/abs/2604.26905

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