{"paper":{"title":"Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mario Fuest, Xinru Cao","submitted_at":"2026-06-16T14:52:21Z","abstract_excerpt":"We consider the Neumann initial boundary value problem associated to the chemotaxis system \\begin{align}\\label{prob:abstract}\\tag{$\\star$} \\begin{cases} u_t = \\big((u+1)^{m-1} u_x - u(u+1)^m v_x\\big)_x & \\text{in $(0, 1) \\times (0, \\infty)$}, \\\\ v_t = v_{xx} - v + u, &\\text{in $(0, 1) \\times (0, \\infty)$}, \\end{cases} \\end{align} where $m \\in \\mathbb R$ is a given parameter. The relation between diffusion and taxis sensitivity is critical since the ratio $u(u+1)^m/(u+1)^{m-1}$ grows like $u^{2/n}$ for large $u$ with $n = \\dim((0, 1)) = 1$. Nonetheless, we show that there is no critical mass ph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18006","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18006/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"}