{"paper":{"title":"On Backward Uniqueness for the Heat Operator in Cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Wu, Wendong Wang","submitted_at":"2013-10-23T15:03:14Z","abstract_excerpt":"Consider the system $|\\partial_tu+\\Delta u|\\leq M(|u|+|\\nabla u|)$, $|u(x,t)|\\leq Me^{M|x|^2}$ in $\\mathcal{C}_{\\theta}\\times[0,T]$ and $u(x,0)=0$ in $\\mathcal{C}_{\\theta}$, where $\\mathcal{C}_{\\theta}$ is a cone with opening angle $\\theta$. L. Escauriaza constructed an example to show that such system has a nonzero bounded solution when $\\theta<90^\\circ$, and it's conjectured that the system has only zero solution for $\\theta>90^\\circ$. Recently Lu Li and V. \\v{S}ver\\'{a}k \\cite{LlS} proved that the claim is true for $\\theta>109.5^\\circ$. Here we improve their result and prove that only zero "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6249","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"}