{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T01:03:36Z","timestamp":1759971816588,"version":"build-2065373602"},"reference-count":36,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T00:00:00Z","timestamp":1758758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Prime Minister\u2019s Research Fellowship","award":["RSPMRF0262"],"award-info":[{"award-number":["RSPMRF0262"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,9,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider a heat equation with memory, which is defined on a bounded domain in ${\\mathbb R}^{d}$ and is driven by $m$ control inputs acting on the interior of the domain. Our objective is to numerically construct a state feedback controller for this equation such that, for each initial state, the solution of the closed-loop system decays exponentially to zero with a decay rate larger than a given rate $\\omega&amp;gt;0$, i.e. we want to solve the $\\omega $-stabilization problem for the heat equation with memory. We first show that the spectrum of the state operator $A$ associated with this equation has an accumulation point at $-\\omega _{0}&amp;lt;0$. Given a $\\omega \\in (0,\\omega _{0})$, we show that the $\\omega $-stabilization problem for the heat equation with memory is solvable provided certain verifiable conditions on the control operator $B$ associated with this equation hold. We then consider an appropriate LQR problem for the heat equation with memory. For each $n\\in{\\mathbb N}$, we construct finite-dimensional approximations $A_{n}$ and $B_{n}$ of $A$ and $B$, respectively, and then show that by solving a corresponding approximation of the LQR problem a feedback operator $K_{n}$ can be computed such that all the eigenvalues of $A_{n} + B_{n} K_{n}$ have real part less than $-\\omega $. We prove that $K_{n}$ for $n$ sufficiently large solves the $\\omega $-stabilization problem for the heat equation with memory. A crucial and nontrivial step in our proof is establishing the uniform (in $n$) stabilizability of the pair $(A_{n}+\\omega I, B_{n})$. We have validated our theoretical results numerically using two examples: an 1D example on a unit interval and a 2D example on a square domain.<\/jats:p>","DOI":"10.1093\/imamci\/dnaf030","type":"journal-article","created":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:48:02Z","timestamp":1759942082000},"source":"Crossref","is-referenced-by-count":0,"title":["LQR based \u03c9-stabilization of a heat equation with memory"],"prefix":"10.1093","volume":"42","author":[{"given":"Bhargav","family":"Pavan Kumar Sistla","sequence":"first","affiliation":[{"name":"Centre for Systems and Control, Indian Institute of Technology Bombay , Mumbai 400076 ,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wasim","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Roorkee , Roorkee 247667 ,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Debanjana","family":"Mitra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Bombay , Mumbai 400076 ,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vivek","family":"Natarajan","sequence":"additional","affiliation":[{"name":"Centre for Systems and Control, Indian Institute of Technology Bombay , Mumbai 400076 ,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,10,8]]},"reference":[{"key":"2025100812475510900_ref1","doi-asserted-by":"crossref","first-page":"939","DOI":"10.3934\/eect.2021032","article-title":"Local stabilization of viscous burgers equation with memory","volume":"11","author":"Akram","year":"2022","journal-title":"Evol. 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