{"paper":{"title":"Fractional heat equations with subcritical absorption having a measure as initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen, Laurent Veron (LMPT), Ying Wang (DIM)","submitted_at":"2014-01-28T14:01:45Z","abstract_excerpt":"We study  existence and uniqueness of   weak solutions to (F) $\\partial\\_t u+ (-\\Delta)^\\alphau+h(t, u)=0 $ in $(0,\\infty)\\times\\R^N$,with initial condition $u(0,\\cdot)=\\nu$ in $\\R^N$, where $N\\ge2$, the operator $(-\\Delta)^\\alpha$is the fractional Laplacian with $\\alpha\\in(0,1)$, $\\nu$ isa bounded Radon measure and $h:(0,\\infty)\\times\\R\\to\\R$ is a continuous function   satisfying a subcritical integrability condition.In particular, if  $h(t,u)=t^\\beta u^p$ with $\\beta\\textgreater{}-1$ and $0 \\textless{} p \\textless{} p^*\\_\\beta:=1+\\frac{2\\alpha(1+\\beta)}{N}$, we prove that there exists a uniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7187","kind":"arxiv","version":3},"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"}