{"paper":{"title":"Lie group classification and invariant exact solutions of the generalized Kompaneets equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Oleksii Patsiuk","submitted_at":"2014-04-04T09:31:46Z","abstract_excerpt":"In this paper, from the group-theoretic point of view it is investigated such class of the generalized Kompaneets equations (GKEs): $$u_t=\\frac1{x^2}\\cdot\\left[x^4(u_x+f(u))\\right]_x, \\ (t,x) \\in \\mathbb{R}_{+} \\times \\mathbb{R}_{+},$$ where $u=u(t,x)$, $u_t=\\frac{\\partial u}{\\partial t}$, $u_x=\\frac{\\partial u}{\\partial x}$, $u_{xx}=\\frac{\\partial^2 u}{\\partial x^2}$; $f(u)$ is an arbitrary smooth function of the variable $u$. Using the Lie--Ovsiannikov algorithm, the group classification of the class under study is carried out. It is shown that the kernel algebra of the full groups of the GK"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1902","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"}