{"paper":{"title":"Approximate controllabilty from the exterior of space-time fractional diffusive equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahamadi Warma","submitted_at":"2018-02-22T13:17:32Z","abstract_excerpt":"Let $\\Om\\subset\\RR^N$ a bounded domain with a Lipschitz continuous boundary. We study the controllability of the space-time fractional diffusion equation \\begin{equation*} \\begin{cases} \\mathbb D_t^\\alpha u+(-\\Delta)^su=0\\;\\;&\\mbox{ in }\\;(0,T)\\times\\Omega\\\\ u=g &\\mbox{ in }\\;(0,T)\\times(\\RR^N\\setminus\\Omega)\\\\ u(0,\\cdot)=u_0&\\mbox{ in }\\;\\Omega, \\end{cases} \\end{equation*} where $u=u(t,x)$ is the state to be controlled and $g=g(t,x)$ is the control function which is localized in a subset $\\mathcal O$ of $\\Omc$. Here, $0<\\alpha\\le 1$, $0<s<1$ and $T>0$ be real numbers. After giving an explicit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08028","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"}