{"paper":{"title":"Optimal cost of fast boundary controls for the one-dimensional heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Pierre Lissy","submitted_at":"2026-08-08T09:57:47Z","abstract_excerpt":"We consider the heat equation on $(0,L)$ with homogeneous Dirichlet condition at one endpoint and a Dirichlet boundary control at the other. If \\(C_{\\mathrm H}(T,L)\\) denotes the optimal \\(L^2\\) null-control cost for initial data in \\(H^{-1}(0,L)\\), we prove that \\[\n  C_{\\mathrm H}(T,L)\n  =\n  \\exp\\left(\\frac{\\kappa_*L^2+o(1)}{T}\\right),\n  \\qquad\n  \\kappa_*\n  =\n  \\frac{\\Gamma(\\frac14)^4}{8\\pi^3}\n  \\simeq\n  0.696601964842838,\n  \\qquad T\\to0^+. \\] The constant \\(\\kappa_*\\) coincides with the upper-bound constant obtained by Dard\\'e and Ervedoza (2019, ANPDE), which was expressed there through a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08041","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/2608.08041/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"}