{"paper":{"title":"The nonlinear stochastic heat equation with rough initial data:a summary of some new results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Le Chen, Robert C. Dalang","submitted_at":"2012-10-05T09:47:40Z","abstract_excerpt":"This is a preliminary announcement of results in the PhD. thesis of the first author concerning the nonlinear stochastic heat equation in the spatial domain $\\R$, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on $\\R$, such as the Dirac delta function, but this measure may also have non-compact support and even be non-tempered (for instance with exponentially growing tails). Existence and uniqueness is proved without appealing to Gronwall's lemma, by keeping tight control over moments in the Picard iterat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1690","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"}