{"paper":{"title":"Ergodicity of reflected stochastic reaction-diffusion equations driven by space-time white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jianliang Zhai, Shijie Shang, Tusheng Zhang","submitted_at":"2026-06-29T10:12:34Z","abstract_excerpt":"We consider the reflected stochastic reaction-diffusion equation on $[0,1]$: \\begin{align*}\n  \\left\\{\n  \\begin{aligned}\n  d u(t,x) &=\\frac{1}{2}\\partial_{xx} u(t,x)dt +b(u(t,x))dt + \\sigma(u(t,x)) W(dt,dx)+L(dt,dx),\\\\\n  u(t,x)&\\geq 0, \\quad t\\geq 0, \\ x\\in [0,1],\\\\\n  u(0,x)&=u_0(x)\\geq 0, \\quad x\\in [0,1],\\\\\n  u(t,0) &= u(t,1) = 0, \\quad \\forall\\ t\\geq 0,\n  \\end{aligned}\n  \\right. \\end{align*} where the initial value $u_0$ is non-negative on $[0,1]$ satisfying $u_0(0)=u_0(1)=0$, and $ W(dt,dx)$ is a space-time white noise. The $L$ in the equation is a random measure on $[0,\\infty)\\times(0,1)$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30080","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/2606.30080/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"}