{"paper":{"title":"Global solvability in a higher-dimensional chemotaxis system for Alopecia Areata: Nonlinear proliferation versus logistic degradation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haotian Tang, Jiashan Zheng","submitted_at":"2025-06-04T04:29:55Z","abstract_excerpt":"This paper is concerned with the Neumann initial-boundary value problem for the chemotaxis system: $u_t=\\Delta u-\\chi_1\\nabla\\cdot(u\\nabla w)+w-\\mu_1u^{r_1}$, $v_t=\\Delta v-\\chi_2\\nabla\\cdot(v\\nabla w)+w+ruv-\\mu_2v^{r_2}$, and $w_t=\\Delta w+u+v-w$ in $\\Omega\\times(0,\\infty)$, which was initially proposed by Dobreva et al. to describe the dynamics of hair loss in Alopecia Areata form. Here, $\\Omega\\subset\\mathbb R^{N}$ $(N\\geq3)$ is a smooth bounded domain, and the parameters fulfill $\\chi_{i}>0$, $\\mu_{i}>0$, $r_{i}\\geq2$ $(i=1,2)$ and $r>0$. The inherent presence of two positive chemotaxis te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03565","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.03565/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}