{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:27:18Z","timestamp":1787318838500,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Basal","award":["FB0008"],"award-info":[{"award-number":["FB0008"]}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-15-CE23-0007"],"award-info":[{"award-number":["ANR-15-CE23-0007"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["3180363"],"award-info":[{"award-number":["3180363"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We investigate the null controllability of the wave equation with a Kelvin--Voigt damping on the two-dimensional torus ${\\mathbb T} ^2$. We consider a distributed control supported in a moving domain $\\omega (t)$ with a uniform motion at a constant velocity $c=(1,\\zeta)$. The results we obtain depend strongly on the topological features of the geodesics of ${\\mathbb T} ^2$ with constant velocity $c$. When $\\zeta\\in {\\mathbb Q}$, writing $\\zeta=p\/q$ with $p,q$ relatively prime, we prove that the null controllability holds if roughly the diameter of $\\omega (0)$ is larger than $1\/p$ and if the control time is larger than $q$. We also prove that for almost every $\\zeta \\in {\\mathbb R}_+\\setminus {\\mathbb Q}$, and also for some particular values including, e.g., $\\zeta=e$, the null controllability holds for any choice of $\\omega (0)$ and for a sufficiently large control time. The proofs rely on a delicate construction of the weight function in a Carleman estimate which gets rid of a topological assumption on the control region often encountered in the literature. Diophantine approximations are also needed when $\\zeta$ is irrational.<\/jats:p>","DOI":"10.1137\/19m1277941","type":"journal-article","created":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T15:09:03Z","timestamp":1610464143000},"page":"131-155","source":"Crossref","is-referenced-by-count":3,"title":["Null Controllability of the Structurally Damped Wave Equation on the Two-Dimensional Torus"],"prefix":"10.1137","volume":"59","author":[{"given":"Patricio","family":"Guzman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lionel","family":"Rosier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,1,12]]},"reference":[{"key":"atypb1","first-page":"15","volume":"22","author":"Albano P.","year":"2000","journal-title":"Electron. J. Differential Equations"},{"key":"atypb2","unstructured":"L. Auslander and R. E. MacKenzie,\n                      Introduction to Differentiable Manifolds\n                      , Dover Publications, Mineola, NY, 2009; reprint of the 1977 edition."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/16M108923X"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2013.05.009"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2019.09.005"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/151004239"},{"key":"atypb7","unstructured":"A. Fursikov and O. Imanuvilov,\n                      Controllability of Evolution Equations\n                      , Lecture Notes Series 34, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University, Korea, 1996."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s12044-015-0262-3"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"M. Golubitsky and V. Guillemin,\n                      Stable Mappings and Their Singularities\n                      , Grad. Texts in Math. 14, Springer-Verlag, New York, Heidelberg, 1973.","DOI":"10.1007\/978-1-4615-7904-5"},{"key":"atypb10","unstructured":"P. Guzm\u00e1n and L. Rosier,\n                      Null Controllability of the Structurally Damped Wave Equation on the Two-dimensional Torus\n                      , 2019, Hal-02159903, 2019,https:\/\/hal.archives-ouvertes.fr\/hal-02159903."},{"key":"atypb11","unstructured":"G. H. Hardy and E. M. Wright,\n                      An Introduction to the Theory of Numbers\n                      , 5th ed., The Clarendon Press, Oxford University Press, New York, 1979."},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"S. Lang,\n                      Introduction to Diophantine Approximations\n                      , 2nd ed., Springer-Verlag, New York, 1995.","DOI":"10.1007\/978-1-4612-4220-8"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2017.05.001"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/110856150"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012999362499"},{"key":"atypb16","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":"atypb17","first-page":"79","volume":"5","author":"Rosier L.","year":"2007","journal-title":"Int. J. Tomogr. Stat."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2008.03.003"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2012.08.014"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1080\/03605300008821507"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1277941","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:42:14Z","timestamp":1787316134000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1277941"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/19M1277941"],"URL":"https:\/\/doi.org\/10.1137\/19m1277941","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}