{"paper":{"title":"Collapsing behaviour of a singular diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui","submitted_at":"2009-10-27T05:50:54Z","abstract_excerpt":"Let $0\\le u_0(x)\\in L^1(\\R^2)\\cap L^{\\infty}(\\R^2)$ be such that $u_0(x) =u_0(|x|)$ for all $|x|\\ge r_1$ and is monotone decreasing for all $|x|\\ge r_1$ for some constant $r_1>0$ and ${ess}\\inf_{\\2{B}_{r_1}(0)}u_0\\ge{ess} \\sup_{\\R^2\\setminus B_{r_2}(0)}u_0$ for some constant $r_2>r_1$. Then under some mild decay conditions at infinity on the initial value $u_0$ we will extend the result of P. Daskalopoulos, M.A. del Pino and N. Sesum \\cite{DP2}, \\cite{DS}, and prove the collapsing behaviour of the maximal solution of the equation $u_t=\\Delta\\log u$ in $\\R^2\\times (0,T)$, $u(x,0)=u_0(x)$ in $\\R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5045","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"}