{"paper":{"title":"Carleman estimate and application to an inverse source problem for a viscoelasticity model in anisotropic case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniela Sforza, Masahiro Yamamoto, Paola Loreti","submitted_at":"2017-01-11T16:43:20Z","abstract_excerpt":"We consider an anisotropic hyperbolic equation with memory term: $$ \\partial_t^2 u(x,t) = \\sum_{i,j=1}^n \\partial_i(a_{ij}(x)\\partial_ju) + \\int^t_0 \\sum_{| \\alpha| \\le 2} b_{\\alpha}(x,t,\\eta)\\partial_x^{\\alpha}u(x,\\eta) d\\eta + F(x,t) $$ for $x \\in \\Omega$ and $t\\in (0,T)$ or $\\in (-T,T)$, which is a model equation for viscoelasticity. First we establish a Carleman estimate for this equation with overdetermining boundary data on a suitable lateral subboundary $\\Gamma \\times (-T,T)$. Second we apply the Carleman estimate to establish a both-sided estimate of $| u(\\cdot,0)|_{H^3(\\Omega)}$ by $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03052","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"}