{"paper":{"title":"A stochastic heat equation with non-locally Lipschitz coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jingyu Huang, Le Chen, Wenxuan Tao","submitted_at":"2025-07-31T15:13:13Z","abstract_excerpt":"We consider the stochastic heat equation (SHE) on the torus $\\mathbb{T}=[0,1]$, driven by space-time white noise $\\dot W$, with an initial condition $u_0$ that is nonnegative and not identically zero:\n  \\begin{equation*}\n  \\frac{\\partial u}{\\partial t} = \\tfrac{1}{2}\\frac{\\partial^2 u}{\\partial x^2} + b(u) + \\sigma(u)\\dot{W}.\n  \\end{equation*} The drift $b$ and diffusion coefficient $\\sigma$ are Lipschitz continuous away from zero, although their Lipschitz constants may blow up as the argument approaches zero. We establish the existence of a unique global mild solution that remains strictly po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23637","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/2507.23637/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"}