{"paper":{"title":"Analysis of a chemotaxis model with indirect signal absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mario Fuest","submitted_at":"2019-01-21T15:31:38Z","abstract_excerpt":"We consider the chemotaxis model \\begin{align*} \\begin{cases} u_t = \\Delta u - \\nabla \\cdot (u \\nabla v), \\\\ v_t = \\Delta v - vw, \\\\ w_t = -\\delta w + u \\end{cases} \\end{align*} in smooth, bounded domains $\\Omega \\subset \\mathbb R^n$, $n \\in \\mathbb N$, where $\\delta \\gt 0$ is a given parameter. If either $n \\le 2$ or $\\|v_0\\|_{L^\\infty(\\Omega)} \\le \\frac1{3n}$ we show the existence of a unique global classical solution $(u, v, w)$ and convergence of $(u(\\cdot, t), v(\\cdot, t), w(\\cdot, t))$ towards a spatially constant equilibrium, as $t \\to \\infty$. The proof of global existence for the case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06962","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}