{"paper":{"title":"Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriele Grillo, Juan Luis Vazquez, Matteo Bonforte","submitted_at":"2008-05-30T13:16:01Z","abstract_excerpt":"We consider the asymptotic behaviour of positive solutions $u(t,x)$ of the fast diffusion equation $u_t=\\Delta (u^{m}/m)={\\rm div} (u^{m-1}\\nabla u)$ posed for $x\\in\\RR^d$, $t>0$, with a precise value for the exponent $m=(d-4)/(d-2)$. The space dimension is $d\\ge 3$ so that $m<1$, and even $m=-1$ for $d=3$. This case had been left open in the general study \\cite{BBDGV} since it requires quite different functional analytic methods, due in particular to the absence of a spectral gap for the operator generating the linearized evolution.\n  The linearization of this flow is interpreted here as the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.4750","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"}