{"paper":{"title":"On some properties of a class of fractional stochastic heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kuanhou Tian, Mohammud Foondun, Wei Liu","submitted_at":"2014-04-27T17:13:01Z","abstract_excerpt":"We consider nonlinear parabolic stochastic equations of the form $\\partial_t u=\\sL u + \\lambda \\sigma(u)\\dot \\xi$ on the ball $B(0,\\,R)$, where $\\dot \\xi$ denotes some Gaussian noise and $\\sigma$ is Lipschitz continuous. Here $\\sL$ corresponds to an $\\alpha$-stable process killed upon exiting $B(0, R)$. We will consider two types of noise; space-time white noise and spatially correlated noise. Under a linear growth condition on $\\sigma$, we study growth properties of the second moment of the solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6791","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"}