{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,19]],"date-time":"2023-03-19T00:11:38Z","timestamp":1679184698225},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T00:00:00Z","timestamp":1675641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"State of Upper Austria and Austrian Science Fund","award":["P 33432-NBL"],"award-info":[{"award-number":["P 33432-NBL"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,3,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is shown that an oblique projection-based feedback control is able to stabilize the state of the Kuramoto\u2013Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The actuators consist of a finite number of indicator functions supported in small subdomains. Simulations are presented, in the one-dimensional case under periodic boundary conditions and in the two-dimensional case under Neumann boundary conditions, showing the stabilizing performance of the feedback control.<\/jats:p>","DOI":"10.1093\/imamci\/dnac033","type":"journal-article","created":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T23:39:33Z","timestamp":1671838773000},"page":"38-80","source":"Crossref","is-referenced-by-count":0,"title":["Feedback semiglobal stabilization to trajectories for the Kuramoto\u2013Sivashinsky equation"],"prefix":"10.1093","volume":"40","author":[{"given":"S\u00e9rgio S","family":"Rodrigues","sequence":"first","affiliation":[{"name":"Johann Radon Institute for Computational and Applied Mathematics , \u00d6AW, Altenbergerstr. 69, 4040 Linz , Austria"}]},{"given":"Dagmawi A","family":"Seifu","sequence":"additional","affiliation":[{"name":"Johann Radon Institute for Computational and Applied Mathematics , \u00d6AW, Altenbergerstr. 69, 4040 Linz , Austria"}]}],"member":"286","published-online":{"date-parts":[[2023,2,6]]},"reference":[{"key":"2023031512452234800_","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s00332-021-09748-8","article-title":"Global solutions of the two-dimensional Kuramoto\u2013Sivashinsky equation with a linearly growing mode in each direction","volume":"31","author":"Ambrose","year":"2021","journal-title":"J. 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