{"paper":{"title":"Global well-posedness to stochastic reaction-diffusion equations on the real line $\\mathbb{R}$ with superlinear drifts driven by multiplicative space-time white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shijie Shang, Tusheng Zhang","submitted_at":"2021-06-05T12:10:29Z","abstract_excerpt":"Consider the stochastic reaction-diffusion equation with logarithmic nonlinearity driven by space-time white noise: \\begin{align}\\label{1.a} \\left\\{ \\begin{aligned} & \\mathrm{d}u(t,x) = \\frac{1}{2}\\Delta u(t,x)\\,\\mathrm{d}t+ b(u(t,x)) \\,\\mathrm{d}t \\nonumber\\\\ & ~~~~~~~~~~~~~~~~ + \\sigma(u(t,x)) \\,W(\\mathrm{d}t,\\mathrm{d}x), \\ t>0, x\\in I , \\\\ & u(0,x)=u_0(x), \\quad x\\in I .\\nonumber \\end{aligned} \\right. \\end{align} When $I$ is a compact interval, say $I=[0,1]$, the well-posedness of the above equation was established in [DKZ] (Ann. Prob. 47:1,2019). The case where $I=\\mathbb{R}$ was left ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.02879","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/2106.02879/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"}