{"paper":{"title":"Critical exponent for semilinear damped wave equations with weighted nonlinear terms and data from Sobolev spaces of negative order","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dinh Van Duong, Tuan Anh Dao","submitted_at":"2025-08-11T09:38:00Z","abstract_excerpt":"In this paper, we would like to study the critical exponent for semilinear damped wave equations with the nonlinearity terms of Coulomb-type singularities $|x|^{-\\alpha} |u(t,x)|^p$ and the initial data belonging to Sobolev spaces of negative order $\\dot{H}^{-\\beta}$. Precisely, we obtain a critical exponent $$p_{\\rm c}(\\alpha,\\beta,n): = 1 + \\frac{4-2\\alpha}{n+2\\beta} $$ for $1 \\leq n \\leq 4$ and $ 0 \\leq \\alpha, \\beta < n/2,$ by proving the global (in time) existence of small data solutions when $p \\geq p_{\\rm c}(\\alpha,\\beta,n)$ and the blow-up result for weak solutions in finite time even "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07802","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.07802/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"}