{"paper":{"title":"Eternal solutions to a singular diffusion equation with critical gradient absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Philippe Laurencot (IMT), Razvan Gabriel Iagar (IMAR)","submitted_at":"2012-01-16T10:14:54Z","abstract_excerpt":"The existence of nonnegative radially symmetric eternal solutions of exponential self-similar type $u(t,x)=e^{-p\\beta t/(2-p)} f_\\beta(|x|e^{-\\beta t};\\beta)$ is investigated for the singular diffusion equation with critical gradient absorption\n\\partial_{t} u-\\Delta_{p} u+|\\nabla u|^{p/2}=0 \\quad \\;\\;\\hbox{in}\\;\\; (0,\\infty)\\times\\real^N\nwhere $2N/(N+1) < p < 2$. Such solutions are shown to exist only if the parameter $\\beta$ ranges in a bounded interval $(0,\\beta_*]$ which is in sharp contrast with well-known singular diffusion equations such as $\\partial_{t}\\phi-\\Delta_{p} \\phi=0$ when $p=2N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3196","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"}