{"paper":{"title":"Nonexplosion for a large class of superlinear stochastic parabolic equations, in arbitrary spatial dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael Salins, Yuyang Zhang","submitted_at":"2025-05-02T02:11:13Z","abstract_excerpt":"This paper explores the finite time explosion of the stochastic parabolic equation $\\frac{\\partial u}{\\partial t}(t,x)=Au(t,x)+\\sigma(u(t,x))\\dot{W}(t,x)$ in arbitrary bounded spatial domain with a large class of space-time colored noise under Neumann, periodic or Dirichlet boundary conditions where $A$ is second-order self-adjoint elliptic operator and $\\sigma$ grows like $\\sigma(u)\\approx C(1+|u|^{\\chi})$ where $\\chi=1+\\frac{1-\\eta}{2\\beta}$ with $\\eta$ and $\\beta$ are the parameters related to the singularities of heat kernel and noise covariance kernel. We improve upon previous results by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00954","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":""},"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"}