{"paper":{"title":"Spreading Speeds and Traveling waves of a parabolic-elliptic chemotaxis system with logistic source on R^N","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Rachidi Salako, Wenxian Shen","submitted_at":"2016-09-17T20:50:41Z","abstract_excerpt":"In this paper, we study the spreading speeds and traveling wave solutions of the PDE $$ \\begin{cases} u_{t}= \\Delta u-\\chi \\nabla \\cdot (u \\nabla v) + u(1-u),\\ \\ x\\in\\mathbb{R}^N 0=\\Delta v-v+u, \\ \\ x\\in\\mathbb{R}^N, \\end{cases} $$ where $u(x,t)$ and $v(x,t)$ represent the population and the chemoattractant densities, respectively, and $\\chi$ is the chemotaxis sensitivity. It has been shown in an earlier work by the authors of the current paper that, when $0<\\chi<1$, for every nonnegative uniformly continuous and bounded function $u_0(x)$, the system has a unique globally bounded classical sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05387","kind":"arxiv","version":3},"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"}