{"paper":{"title":"A heat transfer with a source: the complete set of invariant difference schemes","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Roman Kozlov, Vladimir Dorodnitsyn","submitted_at":"2003-09-08T02:26:59Z","abstract_excerpt":"In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation u_{t}=(K(u)u_{x})_{x}+Q(u). All special cases of K(u) and Q(u) that extend the symmetry group admitted by the differential equation are considered. This paper completes the paper [J. Phys. A: Math. Gen. 30, no. 23 (1997) 8139-8155], where a few invariant models for heat transfer equations were presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309139","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"}