{"paper":{"title":"Asymptotic behaviour of solutions of the fast diffusion equation near its extinction time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui","submitted_at":"2014-07-10T05:37:13Z","abstract_excerpt":"Let $n\\ge 3$, $0<m<\\frac{n-2}{n}$, $\\rho_1>0$, $\\beta\\ge\\frac{m\\rho_1}{n-2-nm}$ and $\\alpha=\\frac{2\\beta+\\rho_1}{1-m}$. For any $\\lambda>0$, we will prove the existence and uniqueness (for $\\beta\\ge\\frac{\\rho_1}{n-2-nm}$) of radially symmetric singular solution $g_{\\lambda}\\in C^{\\infty}(R^n\\setminus\\{0\\})$ of the elliptic equation $\\Delta v^m+\\alpha v+\\beta x\\cdot\\nabla v=0$, $v>0$, in $R^n\\setminus\\{0\\}$, satisfying $\\displaystyle\\lim_{|x|\\to 0}|x|^{\\alpha/\\beta}g_{\\lambda}(x)=\\lambda^{-\\frac{\\rho_1}{(1-m)\\beta}}$. When $\\beta$ is sufficiently large, we prove the higher order asymptotic beha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2696","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"}