{"paper":{"title":"Fujita-type blow-up for inhomogeneous semilinear heat equations with regularly varying forcing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mohamed Majdoub, Vishvesh Kumar","submitted_at":"2026-06-30T13:24:20Z","abstract_excerpt":"We develop a unified framework for Fujita-type blow-up of solutions to the inhomogeneous semilinear heat equation $$\\partial_tu-\\Delta u=|u|^p+\\mathbf{w}(x), \\qquad (t,x)\\in(0,\\infty)\\times\\mathbb{R}^N, \\qquad u(0, \\cdot)=u_0.$$ The classical integrability assumptions on the forcing term are replaced by quantitative regular variation properties of its spatial mass $$F(R)=\\int\\limits_{|x|\\le R}\\mathbf{w}(x)\\,dx.$$ Using techniques from regular variation theory together with the Mitidieri--Pohozaev test-function method, we establish sharp Fujita-type nonexistence results and identify the critica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31643","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/2606.31643/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"}