{"paper":{"title":"Instantaneous everywhere-blowup of parabolic SPDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Eulalia Nualart, Mohammud Foondun","submitted_at":"2023-05-15T09:00:50Z","abstract_excerpt":"We consider the following stochastic heat equation \\begin{equation*}\n  \\partial_t u(t\\,,x) = \\tfrac12 \\partial^2_x u(t\\,,x) + b(u(t\\,,x)) + \\sigma(u(t\\,,x)) \\dot{W}(t\\,,x), \\end{equation*} defined for $(t\\,,x)\\in(0\\,,\\infty)\\times\\mathbb{R}$, where $\\dot{W}$ denotes space-time white noise. The function $\\sigma$ is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the function $b$ is assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition \\[\n  \\int_1^\\infty\\frac{\\mathrm{d} y}{b(y)}<\\infty \\] implies that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08458","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/2305.08458/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"}