{"paper":{"title":"Uniqueness and convergence on equilibria of the Keller-Segel system with subcritical mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jun Wang, Wen Yang, Zhi-An Wang","submitted_at":"2018-04-10T02:54:56Z","abstract_excerpt":"This paper is concerned with the uniqueness of solutions to the following nonlocal semi-linear elliptic equation \\begin{equation}\\label{ellip}\\tag{$\\ast$} \\Delta u-\\beta u+\\lambda\\frac{e^u}{\\int_{\\Omega}e^u}=0~\\mathrm{in}~\\Omega, \\end{equation} where $\\Omega$ is a bounded domain in $\\mathbb{R}^2$ and $\\beta, \\lambda$ are positive parameters. The above equation arises as the stationary problem of the well-known classical Keller-Segel model describing chemotaxis. For equation \\eqref{ellip} with Neumann boundary condition, we establish an integral inequality and prove that the solution of (\\ref{e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03319","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"}