{"paper":{"title":"Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrique Zuazua, Umberto Biccari","submitted_at":"2016-02-23T14:55:40Z","abstract_excerpt":"This article is devoted to the analysis of control properties for a heat equation with singular potential $\\mu/\\delta^2$, defined on a bounded $C^2$ domain $\\Omega\\subset\\mathbb{R}^N$, where $\\delta$ is the distance to the boundary function. More precisely, we show that for any $\\mu\\leq 1/4$ the system is exactly null controllable using a distributed control located in any open subset of $\\Omega$, while for $\\mu>1/4$ there is no way of preventing the solutions of the equation from blowing-up. The result is obtained applying a new Carleman estimate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07176","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"}