{"paper":{"title":"On the identification of source term in the heat equation from sparse data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"William Rundell, Zhidong Zhang","submitted_at":"2019-08-06T08:37:29Z","abstract_excerpt":"We consider the recovery of a source term $f(x,t)=p(x)q(t)$ for the nonhomogeneous heat equation in $\\Omega\\times (0,\\infty)$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^2$ with smooth boundary $\\partial\\Omega$ from overposed lateral data on a sparse subset of $\\partial\\Omega\\times(0,\\infty)$. Specifically, we shall require a small finite number $N$ of measurement points on $\\partial\\Omega$ and prove a uniqueness result; namely the recovery of the pair $(p,q)$ within a given class, by a judicious choice of $N=2$ points. Naturally, with this paucity of overposed data, the problem is sever"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02015","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02015/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}