{"paper":{"title":"Approximate Controllability of a Class of Partial Integro-Differential Equations of Parabolic Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Amiya K. Pani, Anil Kumar, Mohan C. Joshi","submitted_at":"2016-06-12T07:13:18Z","abstract_excerpt":"In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form \\begin{eqnarray*} \\frac{\\partial y}{\\partial t} + A y &=& \\int_0^t B(t, s) y(s) ds + Gu, \\;\\, t \\in [0, T], \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\, \\hfill{(\\ast)}\\\\ y(0) &=& y_0 \\, \\in X, \\nonumber \\end{eqnarray*} where, $y$ denotes the state space variable, $u$ is the control variable, $A$ is a self adjoint, positive definite linear (not necessarily bounded) operator in a Hilbert space $X$ with dense domain $D(A) \\subset X,$ $B(t,s)$ is an unbounded op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03673","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"}