{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:20:58Z","timestamp":1772295658320,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,10,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nWe investigate the problem of sparse optimal controls for the so-called Schl\u00f6gl model and the FitzHugh\u2013Nagumo system. In these reaction\u2013diffusion equations, traveling wave fronts occur that can be controlled in different ways. The <jats:italic>L<jats:sup>1<\/jats:sup><\/jats:italic>-norm of the distributed\ncontrol is included in the objective functional so that optimal controls exhibit effects of sparsity. We prove the differentiability\nof the control-to-state mapping for both dynamical systems, show the well-posedness of the optimal control problems and derive first-order\nnecessary optimality conditions. Based on them, the sparsity of optimal controls is shown. The theory is illustrated by various numerical\nexamples, where wave fronts or spiral waves are controlled in a desired way.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0016","type":"journal-article","created":{"date-parts":[[2013,10,1]],"date-time":"2013-10-01T02:31:54Z","timestamp":1380594714000},"page":"415-442","source":"Crossref","is-referenced-by-count":62,"title":["Sparse Optimal Control of the Schl\u00f6gl and FitzHugh\u2013Nagumo Systems"],"prefix":"10.1515","volume":"13","author":[{"given":"Eduardo","family":"Casas","sequence":"first","affiliation":[{"name":"1Departmento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n, E.T.S.I. Industriales y de Telecomunicaci\u00f3n, Universidad de Cantabria, Av. Los Castros s\/n, 39005 Santander, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christopher","family":"Ryll","sequence":"additional","affiliation":[{"name":"2Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, 10623 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fredi","family":"Tr\u00f6ltzsch","sequence":"additional","affiliation":[{"name":"3Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, 10623 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/4\/article-p415.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/13\/4\/article-p415.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:44Z","timestamp":1614481424000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0016\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,1]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0016","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,1]]}}}