{"paper":{"title":"Global uniqueness in an inverse problem for time fractional diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eric Soccorsi, Lauri Oksanen, Masahiro Yamamoto, Yavar Kian","submitted_at":"2016-01-05T12:39:19Z","abstract_excerpt":"Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \\geq 2$, with boundary $\\partial M$, we consider an initial boundary value problem for a fractional diffusion equation on $(0,T) \\times M$, $T>0$, with time-fractional Caputo derivative of order $\\alpha \\in (0,1) \\cup (1,2)$. We prove uniqueness in the inverse problem of determining the smooth manifold $(M,g)$ (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solution on a subset of $\\partial M$ at fixed time. In the \"flat\" case where $M$ is a compact "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00810","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"}