{"paper":{"title":"Convergence of the Dirichlet solutions of the very fast diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui, SungHoon Kim","submitted_at":"2010-12-15T03:23:25Z","abstract_excerpt":"For any $-1<m<0$, $\\mu>0$, $0\\le u_0\\in L^{\\infty}(R)$ such that $u_0(x)\\le (\\mu_0 |m||x|)^{\\frac{1}{m}}$ for any $|x|\\ge R_0$ and some constants $R_0>1$ and $0<\\mu_0\\leq \\mu$, and $f,\\,g \\in C([0,\\infty))$ such that $f(t),\\, g(t) \\geq \\mu_0$ on $[0,\\infty)$ we prove that as $R\\to\\infty$ the solution $u^R$ of the Dirichlet problem $u_t=(u^m/m)_{xx}$ in $(-R,R)\\times (0,\\infty)$, $u(R,t)=(f(t)|m|R)^{1/m}$, $u(-R,t)=(g(t)|m|R)^{1/m}$ for all $t>0$, $u(x,0)=u_0(x)$ in $(-R,R)$, converges uniformly on every compact subsets of $R\\times (0,T)$ to the solution of the equation $u_t=(u^m/m)_{xx}$ in $R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3218","kind":"arxiv","version":1},"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"}