{"paper":{"title":"Some non-existence results for a class of stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erkan Nane, Mohammud Foondun, Wei Liu","submitted_at":"2016-11-22T12:53:52Z","abstract_excerpt":"Consider the following stochastic partial differential equation, \\begin{equation*} \\partial_t u_t(x)=\n  \\mathcal{L}u_t(x)+ \\sigma (u_t(x))\\dot F(t,x)\\quad{t>0}\\quad\\text{and}\\quad x\\in R^d. \\end{equation*} The operator $\\mathcal{L}$ is the generator of a strictly stable process and $\\dot F$ is the random forcing term which is assumed to be Gaussian. Under some additional conditions, most notably on $\\sigma$ and the initial condition, we show non-existence of global random field solutions. Our results are new and complement earlier works."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07282","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"}