{"paper":{"title":"A null controllability data assimilation for the bulk-surface heat equation with dynamic boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Javier Ram\\'irez-Ganga","submitted_at":"2026-06-06T02:08:36Z","abstract_excerpt":"We address the inverse problem of reconstructing the state at a final time $T_0$ of a parabolic equation with dynamic boundary conditions of Wentzell type, from a distributed interior observation on a subdomain $\\omega \\subset \\Omega$. Our approach combines (i) a Carleman-type observability inequality for the bulk-surface system, with (ii) a Tikhonov-regularized optimal-control reformulation of the data assimilation problem, and (iii) a fully implementable spatio-temporal discretization based on a Lie splitting that decouples the bulk and surface dynamics. We prove an exact reconstruction theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07942","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.07942/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}