{"paper":{"title":"An inverse problem for the wave equation with one measurement and the pseudorandom noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lauri Oksanen, Matti Lassas, Tapio Helin","submitted_at":"2010-11-10T23:18:02Z","abstract_excerpt":"We consider the wave equation $(\\p_t^2-\\Delta_g)u(t,x)=f(t,x)$, in $\\R^n$, $u|_{\\R_-\\times \\R^n}=0$, where the metric $g=(g_{jk}(x))_{j,k=1}^n$ is known outside an open and bounded set $M\\subset \\R^n$ with smooth boundary $\\p M$. We define a deterministic source $f(t,x)$ called the pseudorandom noise as a sum of point sources, $f(t,x)=\\sum_{j=1}^\\infty a_j\\delta_{x_j}(x)\\delta(t)$, where the points $x_j,\\ j\\in\\Z_+$, form a dense set on $\\p M$. We show that when the weights $a_j$ are chosen appropriately, $u|_{\\R\\times \\p M}$ determines the scattering relation on $\\p M$, that is, it determines "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2527","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"}