{"paper":{"title":"Determining electrical and heat transfer parameters using coupled boundary measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Katsiaryna Krupchyk, Matti Lassas, Samuli Siltanen","submitted_at":"2010-12-14T17:34:22Z","abstract_excerpt":"Let $\\Omega\\subset\\R^n$, $n\\ge 3$, be a smooth bounded domain and consider a coupled system in $\\Omega$ consisting of a conductivity equation $\\nabla \\cdot \\gamma(x) \\nabla u(t,x)=0$ and an anisotropic heat equation $\\kappa^{-1}(x)\\partial_t\\psi(t,x)=\\nabla\\cdot (A(x)\\nabla \\psi(t,x))+(\\gamma\\nabla u(t,x))\\cdot \\nabla u(t,x), \\quad t\\ge 0$. It is shown that the coefficients $\\gamma$, $\\kappa$ and $A=(a_{jk})$ are uniquely determined from the knowledge of the boundary map $u|_{\\partial\\Omega}\\mapsto \\nu\\cdot A\\nabla \\psi|_{\\partial\\Omega}$, where $\\nu$ is the unit outer normal to $\\partial\\Omeg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3099","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"}