{"paper":{"title":"Observability and Control Property for a Singular Heat Equation with Variable Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shumin Li, Xue Qin","submitted_at":"2018-11-13T08:03:06Z","abstract_excerpt":"The goal of this paper is to analyze control properties of the parabolic equation with variable coefficients in the principal part and with a singular inverse-square potential:\\,$\\partial_tu(x,t)-{\\rm div}(p(x)\\nabla u(x,t))-({\\mu}/{|x|^2})u(x,t)=f(x,t).$ Here $\\mu$ is a real constant . It was proved in the paper of Goldstein and Zhang (2003) that the equation is well-posedness when $0\\leq{\\mu\\leq p_1(n-2)^2/4}$, and in this paper, we mainly consider the case $0\\leq\\mu<({ p_1^2}/{ p_2})(n-2)^2/4$ , where $ p_1,p_2$ are two positive constants which satisfy:\\, $ 0< p_1\\leq p(x)\\leq p_2 , \\forall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05780","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"}