{"paper":{"title":"Approximation theorems for parabolic equations and movement of local hot spots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Enciso, Daniel Peralta-Salas, M. \\'Angeles Garc\\'ia-Ferrero","submitted_at":"2017-10-10T18:50:46Z","abstract_excerpt":"We prove a global approximation theorem for a general parabolic operator $L$, which asserts that if $v$ satisfies the equation $Lv=0$ in a spacetime region $\\Omega \\subset \\mathbb{R}^{n+1}$ satisfying certain necessary topological condition, then it can be approximated in a H\\\"older norm by a global solution $u$ to the equation. If $\\Omega$ is compact and $L$ is the usual heat operator, one can instead approximate the local solution $v$ by the unique solution that falls off at infinity to the Cauchy problem with a suitably chosen smooth, compactly supported initial datum. These results are nex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03782","kind":"arxiv","version":2},"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"}