{"paper":{"title":"Recovery of time-dependent coefficient on Riemanian manifold for hyperbolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lauri Oksanen, Yavar Kian","submitted_at":"2016-06-23T09:34:38Z","abstract_excerpt":"Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \\geq 2$, with boundary $\\partial M$, we study the inverse boundary value problem of determining a time-dependent potential $q$, appearing in the wave equation $\\partial_t^2u-\\Delta_g u+q(t,x)u=0$ in $\\bar M=(0,T)\\times M$ with $T>0$. Under suitable geometric assumptions we prove global unique determination of $q\\in L^\\infty(\\bar M)$ given the Cauchy data set on the whole boundary $\\partial \\bar M$, or on certain subsets of $\\partial \\bar M$. Our problem can be seen as an analogue of the Calder\\'on problem on the Lorentzian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07243","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"}