{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:20:08Z","timestamp":1787322008655,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>We study the wave equation on a domain of $\\mathbb{R}^d$, $d\\geq 2$, with dynamical boundary control applied on a part of the boundary and a Dirichlet boundary condition on the remaining part. We prove the asymptotic stability and nonuniform stability of the associated semigroup.<\/jats:p>","DOI":"10.1137\/140971336","type":"journal-article","created":{"date-parts":[[2015,8,27]],"date-time":"2015-08-27T12:46:31Z","timestamp":1440679591000},"page":"2558-2581","source":"Crossref","is-referenced-by-count":26,"title":["The Multidimensional Wave Equation with Generalized Acoustic Boundary Conditions I: Strong Stability"],"prefix":"10.1137","volume":"53","author":[{"given":"Z.","family":"Abbas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Nicaise","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,8,27]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s40324-013-0002-5"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/140971348"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1988-0933321-3"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/0330055"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202513500280"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1976.25.25071"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"B. P. Belinsky,\n                      Wave propagation in the ice-covered ocean wave guide and operator polynomials\n                      , in Proceedings of the Second ISAAC Congress, Vol. 2 (Fukuoka, 1999), Int. Soc. Anal. Appl. Comput. 8, Kluwer Academic, Dordrecht, 2000, pp. 1319-1333.","DOI":"10.1007\/978-1-4613-0271-1_57"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-009-0439-0"},{"key":"atypb9","unstructured":"H. Brezis,\n                      Analyse Fonctionnelle\n                      , Collect. Math. Appl. Ma\\^\\i trise, Masson, Paris, 1983."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1978-0461206-1"},{"key":"atypb11","unstructured":"P. Grisvard,\n                      Elliptic Problems in Nonsmooth Domains\n                      , Monogr. Stud. Math. 24, Pitman, Boston, MA, 1985."},{"key":"atypb12","first-page":"43","volume":"1","author":"Huang F. L.","year":"1985","journal-title":"Ann. Differential Equations"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01182480"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-97-08614-2"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139996314106"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(94)90083-3"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(03)80039-3"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"A. Pazy,\n                      Semigroups of Linear Operators and Applications to Partial Differential Equations\n                      , Appl. Math. Sci. 44, Springer-Verlag, New York, 1983.","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.2307\/1999112"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996300975"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(75)90009-1"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/0331030"},{"key":"atypb23","unstructured":"L. Toufayli,\n                      Stabilisation Polynomiale et Contro\u0302labilite\u0301 Exacte des E\u0301quations des Ondes par des Contro\u0302les Indirects et Dynamiques\n                      , Ph.D. thesis, University of Strasbourg, Strasbourg, France, 2013."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(03)80057-5"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160120202"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/140971336","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:17:04Z","timestamp":1787318224000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/140971336"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/140971336"],"URL":"https:\/\/doi.org\/10.1137\/140971336","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}