{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:34:44Z","timestamp":1760150084797,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T00:00:00Z","timestamp":1697846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we analyze a bilinear optimal control problem related to a 2D parabolic\u2013elliptic chemo-repulsion system with a nonlinear chemical signal production term. We prove the existence of global optimal solutions with bilinear control, and applying a generic result on the existence of Lagrange multipliers in Banach spaces, we obtain first-order necessary optimality conditions and derive an optimality system for a local optimal solution.<\/jats:p>","DOI":"10.3390\/sym15101949","type":"journal-article","created":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T12:59:01Z","timestamp":1697893141000},"page":"1949","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Control Problem Related to a 2D Parabolic\u2013Elliptic Chemo-Repulsion System with Nonlinear Production"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7726-2362","authenticated-orcid":false,"given":"Exequiel","family":"Mallea-Zepeda","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Av. Angamos 0610, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2359-7308","authenticated-orcid":false,"given":"Luis","family":"Medina","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Av. Angamos 601, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,21]]},"reference":[{"key":"ref_1","first-page":"83","article-title":"On some models describing cellular movement: The macroscopic scale","volume":"2","year":"2009","journal-title":"Bol. Soc. Esp. Mat. Apl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1137\/S0036139995288976","article-title":"Aggregation, blowup and collapse: The ABC\u2019S of taxis in reinforced random walks","volume":"57","author":"Othmer","year":"1997","journal-title":"SIAM J. Appl. 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