{"paper":{"title":"Some properties of non-linear fractional stochastic heat equations on bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Erkan Nane, Mohammud Foondun, Ngartelbaye Guerngar","submitted_at":"2016-05-04T15:48:18Z","abstract_excerpt":"Consider the following stochastic partial differential equation, \\begin{equation*} \\partial_t u_t(x)=\n  \\mathcal{L}u_t(x)+ \\xi\\sigma (u_t(x)) \\dot F(t,x), \\end{equation*} where $\\xi$ is a positive parameter and $\\sigma$ is a globally Lipschitz continuous function. The stochastic forcing term $\\dot F(t,x)$ is white in time but possibly colored in space. The operator $\\mathcal{L}$ is a non-local operator. We study the behaviour of the solution with respect to the parameter $\\xi$, extending the results in \\cite{FoonNual} and \\cite{Bin}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01323","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"}