{"paper":{"title":"Unique Determination of Sound Speeds for Coupled Systems of Semi-linear Wave Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alden Waters","submitted_at":"2018-04-30T12:31:06Z","abstract_excerpt":"We consider coupled systems of semi-linear wave equations with different sound speeds on a finite time interval $[0,T]$ and a bounded Lipschitz domain $\\Omega$ in $\\mathbb{R}^3$, with boundary $\\partial\\Omega$. We show the coupled systems are well posed for variable coefficient sounds speeds and short times. Under the assumption of small initial data, we prove the source to solutions map on $[0,T]\\times\\partial\\Omega$ associated with the nonlinear problem is sufficient to determine the source-to-solution map for the linear problem. We can then reconstruct the sound speeds in $\\Omega$ for the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11155","kind":"arxiv","version":2},"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"}