{"paper":{"title":"A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Tomomi Yokota","submitted_at":"2017-01-11T01:01:26Z","abstract_excerpt":"This paper deals with the Keller--Segel system with signal-dependent sensitivity \\begin{equation*} u_t=\\Delta u - \\nabla \\cdot (u \\chi(v)\\nabla v), \\quad v_t=\\Delta v + u - v, \\quad x\\in\\Omega,\\ t>0, \\end{equation*} where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$, $n\\geq 2$; $\\chi$ is a function satisfying $\\chi(s)\\leq K(a+s)^{-k}$ for some $k\\geq 1$ and $a\\geq 0$. In the case that $k=1$, Fujie (J. Math. Anal. Appl.; 2015; 424; 675--684) established global existence of bounded solutions under the condition $K<\\sqrt{\\frac{2}{n}}$. On the other hand, when $k>1$, Winkler (Math. Nachr.; 2010;"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02817","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"}