{"paper":{"title":"Parabolic power concavity and parabolic boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuhiro Ishige, Paolo Salani","submitted_at":"2013-07-24T16:41:27Z","abstract_excerpt":"This paper is concerned with power concavity properties of the solution to the parabolic boundary value problem \\begin{equation} \\tag{$P$} \\left\\{\\begin{array}{ll} \\partial_t u=\\Delta u +f(x,t,u,\\nabla u) & \\mbox{in}\\quad\\Omega\\times(0,\\infty),\\vspace{3pt}\\\\ u(x,t)=0 & \\mbox{on}\\quad\\partial \\Omega\\times(0,\\infty),\\vspace{3pt}\\\\ u(x,0)=0 & \\mbox{in}\\quad\\Omega, \\end{array} \\right. \\end{equation} where $\\Omega$ is a bounded convex domain in ${\\bf R}^n$ and $f$ is a nonnegative continuous function in $\\Omega\\times(0,\\infty)\\times{\\bf R}\\times{\\bf R}^n$. We give a sufficient condition for the sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6482","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"}