{"paper":{"title":"Sharp Lifespan Estimates and Fujita Phenomena for Fractional Hardy-H\\'enon Type Parabolic Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Berikbol T. Torebek, Mohamed Majdoub","submitted_at":"2026-06-25T03:04:39Z","abstract_excerpt":"We study the lifespan of mild solutions to the fractional semilinear parabolic Cauchy problem with a Hardy--H\\'enon-type weight \\[\n  u_t + (-\\Delta)^s u = |x|^{-\\gamma}\\,|u|^p,\n  \\qquad (t,x)\\in(0,\\infty)\\times\\mathbb{R}^N,\n  \\qquad u(0,x)=\\varepsilon\\,u_0(x), \\] where $0<s<1$, $0\\le\\gamma<\\min(2s,N)$, $p>1$ and $u_0\\in L^1\\cap L^\\infty$ with $\\int_{\\mathbb{R}^N}u_0(x)\\,dx>0$. Setting \\[\n  p_F \\;:=\\; 1+\\frac{2s-\\gamma}{N}, \\] we prove that the lifespan $T_\\varepsilon$ obeys, for every sufficiently small $\\varepsilon>0$, \\[\n  T_\\varepsilon \\;\\approx\\;\n  \\begin{cases}\n  \\varepsilon^{-\\,\\beta^{-1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26555","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26555/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}