{"paper":{"title":"Determination of convection terms and quasi-linearities appearing in diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pedro Caro, Yavar Kian","submitted_at":"2018-12-20T11:35:36Z","abstract_excerpt":"We consider the highly nonlinear and ill-posed inverse problem of determining some general expression $F(x,t,u,\\nabla_xu)$ appearing in the diffusion equation $\\partial_tu-\\Delta_x u+F(x,t,u,\\nabla_xu)=0$ on $\\Omega\\times(0,T)$, with $T>0$ and $\\Omega$ a bounded open subset of $\\mathbb R^n$, $n\\geq2$, from measurements of solutions on the lateral boundary $\\partial\\Omega\\times(0,T)$. We consider both linear and nonlinear expression of $F(x,t,u,\\nabla_xu)$. In the linear case, the equation can be seen as a convection-diffusion equation and our inverse problem corresponds to the unique recovery,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08495","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"}