{"paper":{"title":"Solvability of a Keller-Segel system with signal-dependent sensitivity and essentially sublinear production","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Viglialoro, Thomas E. Woolley","submitted_at":"2018-07-26T08:18:50Z","abstract_excerpt":"In this paper we consider the zero-flux chemotaxis-system \\begin{equation*} \\begin{cases} u_{t}=\\Delta u-\\nabla \\cdot (u \\chi(v)\\nabla v) & \\textrm{in}\\quad \\Omega\\times (0,\\infty), \\\\ 0=\\Delta v-v+g(u) & \\textrm{in}\\quad \\Omega\\times (0,\\infty),\\\\ \\end{equation*} in a smooth and bounded domain $\\Omega$ of $\\mathbb{R}^2$. The chemotactic sensitivity $\\chi$ is a general nonnegative function from $C^1((0,\\infty))$ whilst $g$, the production of the chemical signal $v$, belongs to $C^1([0,\\infty))$ and satisfies $\\lambda_1\\leq g(s)\\leq \\lambda_2(1+s)^\\beta$, for all $s\\geq 0$, $0\\leq\\beta\\leq \\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10005","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"}