{"paper":{"title":"Uniqueness and stability of an inverse problem for a semi-linear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Leyter Potenciano-Machado, Matti Lassas, Teemu Tyni, Tony Liimatainen","submitted_at":"2020-06-23T17:46:31Z","abstract_excerpt":"We consider the recovery of a potential associated with a semi-linear wave equation on $\\mathbb{R}^{n+1}$, $n\\geq 1$. We show a H\\\"older stability estimate for the recovery of an unknown potential $a$ of the wave equation $\\square u +a u^m=0$ from its Dirichlet-to-Neumann map. We show that an unknown potential $a(x,t)$, supported in $\\Omega\\times[t_1,t_2]$, of the wave equation $\\square u +a u^m=0$ can be recovered in a H\\\"older stable way from the map $u|_{\\partial \\Omega\\times [0,T]}\\mapsto \\langle\\psi,\\partial_\\nu u|_{\\partial \\Omega\\times [0,T]}\\rangle_{L^2(\\partial \\Omega\\times [0,T])}$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.13193","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.13193/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}