Some Progress in Global Existence of Solutions to a Higher-Dimensional Chemotaxis System Modeling Alopecia Areata

    June 2025 in “ arXiv (Cornell University) ”
    H.Y. Tang, Jiashan Zheng
    TLDR The system can have a stable solution under certain conditions, helping understand hair loss in Alopecia Areata.
    This paper investigates the global existence of solutions in a chemotaxis system modeling Alopecia Areata, focusing on logistic damping effects. The study demonstrates that under certain conditions, such as when $r_{1}=r_{2}=2$ and $\min\{μ_{1},μ_{2}\}$ exceeds a specific threshold $μ^{\star}$, or when $r_{i}>2$, the system admits a unique classical solution that remains globally bounded for all smooth initial data. The research provides new insights into the weak solution theory and highlights the role of the logistic source in preventing solution blow-ups, contributing to the understanding of hair loss dynamics in Alopecia Areata.
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