{"paper":{"title":"Determination of time-dependent coefficients for a hyperbolic inverse problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ricardo Salazar","submitted_at":"2010-09-21T06:07:21Z","abstract_excerpt":"We consider an inverse boundary value problem for the hyperbolic partial differential equation $ (-i\\partial_{t} + A_{0}(t,x))^2 u(t,x) - \\sum_{j=1}^n (-i\\partial_{x_j} + A_{j}(t,x))^2 u(t,x) + V(t,x)u(t,x) = 0 $ with time dependent vector and scalar potentials ($\\mathcal{A}= (A_{0},...,A_{m})$ and $V(t,x)$ respectively) on a bounded, smooth cylindric domain $(-\\infty,\\infty)\\times\\Omega$. Using a geometric optics construction we show that the boundary data allows us to recover integrals of the potentials along `light rays' and we then establish the uniqueness of these potentials modulo a gaug"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4003","kind":"arxiv","version":4},"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"}