{"paper":{"title":"Large time behavior of solutions of Trudinger's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erik Lindgren, Ryan Hynd","submitted_at":"2017-02-06T14:39:03Z","abstract_excerpt":"We study the large time behavior of solutions $v:\\Omega\\times(0,\\infty)\\rightarrow \\mathbb{R}$ of the PDE $\\partial_t(|v|^{p-2}v)=\\Delta_pv.$ We show that $e^{\\left(\\lambda_p/(p-1)\\right)t}v(x,t)$ converges to an extremal of a Poincar\\'e inequality on $\\Omega$ with optimal constant $\\lambda_p$, as $t\\rightarrow \\infty$. We also prove that the large time values of solutions approximate the extremals of a corresponding \"dual\" Poincar\\'e inequality on $\\Omega$. Moreover, our theory allows us to deduce the large time asymptotics of related doubly nonlinear flows involving various boundary conditio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01630","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"}