{"paper":{"title":"Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $\\mathbb{R}^{N}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.AP","authors_text":"Rachidi Salako, Wenxian Shen","submitted_at":"2016-08-05T22:05:05Z","abstract_excerpt":"In the current paper, we consider the following parabolic-elliptic semilinear Keller-Segel model on $\\mathbb{R}^{N}$, \\begin{equation*} \\begin{cases} u_{t}=\\nabla\\cdot (\\nabla u-\\chi u\\nabla v)+a u -b u^2, \\quad x\\in\\mathbb{R}^N,\\,\\, t>0\\cr 0=(\\Delta- I)v+ u, \\quad x\\in\\mathbb{R}^N,\\,\\, t>0, \\end{cases} \\end{equation*} where $ \\chi >0, \\ a\\ge 0,\\ b> 0$ are constant real numbers and $N$ is a positive integer. We first prove the local existence and uniqueness of classical solutions $(u(x,t;u_0),v(x,t;u_0))$ with $u(x,0;u_0)=u_0(x)$ for various initial functions $u_0(x)$. Next, under some conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02031","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"}