{"paper":{"title":"The fast signal diffusion limit in a chemotaxis system with strong signal sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami","submitted_at":"2017-11-05T23:41:35Z","abstract_excerpt":"This paper gives a first insight into making a mathematical bridge between the parabolic-parabolic signal-dependent chemotaxis system and its parabolic-elliptic version. To be more precise, this paper deals with convergence of a solution for the parabolic-parabolic chemotaxis system with strong signal sensitivity $$ (u_\\lambda)_t = \\Delta u_\\lambda - \\nabla \\cdot (u_\\lambda \\chi(v_\\lambda)\\nabla u_\\lambda), \\quad \\lambda (v_\\lambda)_t = \\Delta v_\\lambda - v_\\lambda +u_\\lambda \\quad \\mbox{in} \\ \\Omega\\times (0,\\infty) $$ to that for the parabolic-elliptic chemotaxis system $$ u_t = \\Delta u -\\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01677","kind":"arxiv","version":2},"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"}