{"paper":{"title":"Global solutions to reaction-diffusion equations with super-linear drift and multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Robert C. Dalang, Tusheng Zhang","submitted_at":"2017-01-17T13:22:57Z","abstract_excerpt":"Let $\\xi(t\\,,x)$ denote space-time white noise and consider a reaction-diffusion equation of the form \\[\n  \\dot{u}(t\\,,x)=\\tfrac12 u\"(t\\,,x) + b(u(t\\,,x)) + \\sigma(u(t\\,,x)) \\xi(t\\,,x), \\] on $\\mathbb{R}_+\\times[0\\,,1]$, with homogeneous Dirichlet boundary conditions and suitable initial data, in the case that there exists $\\varepsilon>0$ such that $\\vert b(z)\\vert \\ge|z|(\\log|z|)^{1+\\varepsilon}$ for all sufficiently-large values of $|z|$. When $\\sigma\\equiv 0$, it is well known that such PDEs frequently have non-trivial stationary solutions. By contrast, Bonder and Groisman (2009) have recen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04660","kind":"arxiv","version":2},"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"}