{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T18:11:23Z","timestamp":1759342283376},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2013,9,20]],"date-time":"2013-09-20T00:00:00Z","timestamp":1379635200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2014,8]]},"DOI":"10.1007\/s10444-013-9320-5","type":"journal-article","created":{"date-parts":[[2013,9,19]],"date-time":"2013-09-19T10:29:52Z","timestamp":1379586592000},"page":"711-745","source":"Crossref","is-referenced-by-count":3,"title":["Numerical observers with vanishing viscosity for the 1d wave equation"],"prefix":"10.1007","volume":"40","author":[{"given":"Galina C.","family":"Garc\u00eda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tak\u00e9o","family":"Takahashi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,9,20]]},"reference":[{"issue":"12","key":"9320_CR1","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1016\/j.crma.2005.05.006","volume":"340","author":"D Auroux","year":"2005","unstructured":"Auroux, D., Blum, J.: Back and forth nudging algorithm for data assimilation problems. C. R. Math. Acad. Sci. Paris 340(12), 873\u2013878 (2005)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"9320_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-0348-6418-3_1","volume-title":"Estimation and Control of Distributed Parameter Systems (Vorau, 1990) of International Series of Numerical Mathematics, vol. 100","author":"HT Banks","year":"1991","unstructured":"Banks, H.T., Ito, K., Wang, C.: Exponentially stable approximations of weakly damped wave equations. In: Estimation and Control of Distributed Parameter Systems (Vorau, 1990) of International Series of Numerical Mathematics, vol. 100, pp. 1\u201333. Birkh\u00e4user, Basel (1991)"},{"issue":"5","key":"9320_CR3","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1137\/0330055","volume":"30","author":"C Bardos","year":"1992","unstructured":"Bardos, C., Lebeau, G., Rauch, J.: Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control Optim. 30(5), 1024\u20131065 (1992)","journal-title":"SIAM J. Control Optim."},{"key":"9320_CR4","unstructured":"Bensoussan, A.: Filtrage Optimal des Syst\u00e8mes Lin\u00e9aires. Dunod (1971)"},{"key":"9320_CR5","unstructured":"Brezis, H.: Analyse fonctionnelle. Collection Math\u00e9matiques Appliqu\u00e9es pour la Ma\u00eetrise, [Collection of Applied Mathematics for the Master\u2019s Degree]. Masson, Paris. Th\u00e9orie et applications, [Theory and applications] (1983)"},{"issue":"12","key":"9320_CR6","doi-asserted-by":"crossref","first-page":"1250040, 35","DOI":"10.1142\/S0218202512500406","volume":"22","author":"D Chapelle","year":"2012","unstructured":"Chapelle, D., C\u00eendea, N., Moireau, P.: Improving convergence in numerical analysis using observers\u2014the wave-like equation case. Math. Models Methods Appl. Sci. 22(12), 1250040, 35 (2012)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"9320_CR7","unstructured":"Chapelle, D., C\u00eendea, N., De Buhan, M., Moireau, P.: Exponential convergence of an observer based on partial field measurements for the wave equation. Math. Probl. Eng. , 12 (2012). Art. ID 581053"},{"issue":"3","key":"9320_CR8","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1137\/09077641X","volume":"49","author":"N C\u00eendea","year":"2011","unstructured":"C\u00eendea, N., Micu, S., Tucsnak, M.: An approximation method for exact controls of vibrating systems. SIAM J. Control Optim. 49(3), 1283\u20131305 (2011)","journal-title":"SIAM J. Control Optim."},{"key":"9320_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4224-6","volume-title":"An Introduction to Infinite-Dimensional Linear Systems Theory, of Texts in Applied Mathematics, vol. 21","author":"RF Curtain","year":"1995","unstructured":"Curtain, R.F., Zwart, H.: An Introduction to Infinite-Dimensional Linear Systems Theory, of Texts in Applied Mathematics, vol. 21. Springer, New York (1995)"},{"key":"9320_CR10","unstructured":"Deguenon, J., Sallet, G., Xu, C.-Z.: Infinite dimensional observers for vibrating systems. In: Proceedings of IEEE Conference on Decision and Control, pp. 3979\u20133983 (2006)"},{"issue":"1","key":"9320_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF03167891","volume":"7","author":"R Glowinski","year":"1990","unstructured":"Glowinski, R., Li, C.H., Lions, J.-L.: A numerical approach to the exact boundary controllability of the wave equation. I. Dirichlet controls: description of the numerical methods. Japan J. Appl. Math. 7(1), 1\u201376 (1990)","journal-title":"Japan J. Appl. Math."},{"key":"9320_CR12","unstructured":"Haine, G.: Recovering the initial data of an evolution equation. Application to thermoacoustic tomography. Submitted (2012)"},{"key":"9320_CR13","unstructured":"Haine, G.: Recovering the observable part of the initial data of an infinite-dimensional linear system. Submitted (2012)"},{"issue":"7\u201310","key":"9320_CR14","first-page":"715","volume":"45","author":"G Haine","year":"2011","unstructured":"Haine, G., Ramdani, K.: Observateurs it\u00e9ratifs en horizon fini. Application \u00e0 la reconstruction de donn\u00e9es initiales pour des edp d\u2019\u00e9volution. J. Eur. Syst. Autom. (JESA) 45(7\u201310), 715\u2013724 (2011)","journal-title":"J. Eur. Syst. Autom. (JESA)"},{"issue":"2","key":"9320_CR15","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s00211-011-0408-x","volume":"120","author":"G Haine","year":"2012","unstructured":"Haine, G., Ramdani, K.: Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations. Numer. Math. 120(2), 307\u2013343 (2012)","journal-title":"Numer. Math."},{"issue":"6","key":"9320_CR16","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/S0764-4442(98)80036-0","volume":"326","author":"J-A Infante","year":"1998","unstructured":"Infante, J.-A., Zuazua, E.: Boundary observability for the space-discretizations of the 1-d wave equation. C. R. Acad. Sci. Paris S\u00e9r. I Math. 326(6), 713\u2013718 (1998)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"issue":"2","key":"9320_CR17","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1051\/m2an:1999123","volume":"33","author":"JA Infante","year":"1999","unstructured":"Infante, J.A., Zuazua, E.: Boundary observability for the space semi-discretizations of the 1-D wave equation. M2AN Math. Model. Numer. Anal. 33(2), 407\u2013438 (1999)","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"3","key":"9320_CR18","doi-asserted-by":"crossref","first-page":"641","DOI":"10.3934\/dcdss.2011.4.641","volume":"4","author":"K Ito","year":"2011","unstructured":"Ito, K., Ramdani, K., Tucsnak, M.: A time reversal based algorithm for solving initial data inverse problems. Discrete Contin. Dyn. Syst. Ser. S 4(3), 641\u2013652 (2011)","journal-title":"Discrete Contin. Dyn. Syst. Ser. S"},{"key":"9320_CR19","unstructured":"Kailath, T., Sayed, A.H., Babak, H.: Linear Estimation. Prentice Hall (2000)"},{"key":"9320_CR20","unstructured":"Komornik, V.: Exact controllability and stabilization. The multiplier method. In: RAM: Research in Applied Mathematics. Masson, Paris (1994)"},{"key":"9320_CR21","doi-asserted-by":"crossref","unstructured":"Li, X.-D., Xu, C.-Z., Peng, Y.-J., Tucsnak, M.: On the numerical investigation of a Luenberger type observer for infinite-dimensional vibrating systems. In: Proceedings of the 17th World Congress The International Federation of Automatic Control, pp. 7624\u20137629. Seoul, Cor\u00e9e, R\u00e9publique De (2008)","DOI":"10.3182\/20080706-5-KR-1001.01289"},{"key":"9320_CR22","unstructured":"Lions, J.-L.: Contr\u00f4labilit\u00e9 Exacte, Perturbations et Stabilisation de Syst\u00e8mes Distribu\u00e9s. Tome 2, Recherches en Math\u00e9matiques Appliqu\u00e9es [Research in Applied Mathematics] vol. 9. Masson, Paris (1988). Perturbations. [Perturbations]"},{"issue":"6","key":"9320_CR23","doi-asserted-by":"crossref","first-page":"2857","DOI":"10.1137\/070696933","volume":"47","author":"S Micu","year":"2008","unstructured":"Micu, S.: Uniform boundary controllability of a semidiscrete 1-D wave equation with vanishing viscosity. SIAM J. Control Optim. 47(6), 2857\u20132885 (2008)","journal-title":"SIAM J. Control Optim."},{"issue":"6\u20138","key":"9320_CR24","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1016\/j.cma.2007.08.021","volume":"197","author":"P Moireau","year":"2008","unstructured":"Moireau, P., Chapelle, D., Le Tallec, P.: Joint state and parameter estimation for distributed mechanical systems. Comput. Methods Appl. Mech. Eng. 197(6\u20138), 659\u2013677 (2008)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"2","key":"9320_CR25","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1051\/m2an:2005012","volume":"39","author":"A M\u00fcnch","year":"2005","unstructured":"M\u00fcnch, A.: A uniformly controllable and implicit scheme for the 1-D wave equation. M2AN Math. Model. Numer. Anal. 39(2), 377\u2013418 (2005)","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"3\u20134","key":"9320_CR26","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/S0167-6911(02)00271-2","volume":"48","author":"M Negreanu","year":"2003","unstructured":"Negreanu, M., Zuazua, E.: Uniform boundary controllability of a discrete 1-D wave equation. Optimization and control of distributed systems. Syst. Control Lett. 48(3\u20134), 261\u2013279 (2003)","journal-title":"Syst. Control Lett."},{"issue":"1","key":"9320_CR27","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1137\/050630015","volume":"44","author":"M Negreanu","year":"2006","unstructured":"Negreanu, M., Zuazua, E.: Discrete Ingham inequalities and applications. SIAM J. Numer. Anal. 44(1), 412\u2013448 (2006). (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"9320_CR28","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s10444-008-9108-1","volume":"32","author":"S Nicaise","year":"2010","unstructured":"Nicaise, S., Valein, J.: Quasi exponential decay of a finite difference space discretization of the 1-d wave equation by pointwise interior stabilization. Adv. Comput. Math. 32(3), 303\u2013334 (2010)","journal-title":"Adv. Comput. Math."},{"issue":"6","key":"9320_CR29","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1137\/070684823","volume":"68","author":"KD Phung","year":"2008","unstructured":"Phung, K.D., Zhang, X.: Time reversal focusing of the initial state for Kirchhoff plate. SIAM J. Appl. Math. 68(6), 1535\u20131556 (2008)","journal-title":"SIAM J. Appl. Math."},{"issue":"1","key":"9320_CR30","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.matpur.2005.10.006","volume":"85","author":"K Ramdani","year":"2006","unstructured":"Ramdani, K., Takahashi, T., Tucsnak, M.: Internal stabilization of the plate equation in a square: the continuous and the semi-discretized problems. J. Math. Pures Appl. (9) 85(1), 17\u201337 (2006)","journal-title":"J. Math. Pures Appl. (9)"},{"key":"9320_CR31","doi-asserted-by":"crossref","unstructured":"Ramdani, K., Takahashi, T., Tucsnak, M.: Semi-discr\u00e9tisation en espace du probl\u00e8me de la stabilisation interne de l\u2019\u00e9quation des poutres. In: Paris-Sud Working Group on Modelling and Scientific Computing 2006\u20132007, of ESAIM Proceedings, vol. 18, pp. 48\u201356. EDP Sci., Les Ulis (2007)","DOI":"10.1051\/proc:071805"},{"issue":"3","key":"9320_CR32","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1051\/cocv:2007020","volume":"13","author":"K Ramdani","year":"2007","unstructured":"Ramdani, K., Takahashi, T., Tucsnak, M.: Uniformly exponentially stable approximations for a class of second order evolution equations\u2014application to LQR problems. ESAIM Control Optim. Calc. Var. 13(3), 503\u2013527 (2007)","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"9320_CR33","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1016\/j.automatica.2010.06.032","volume":"46","author":"K Ramdani","year":"2010","unstructured":"Ramdani, K., Tucsnak, M., Weiss, G.: Recovering the initial state of an infinite-dimensional system using observers. Automatica 46, 1616\u20131625 (2010)","journal-title":"Automatica"},{"issue":"3","key":"9320_CR34","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s00211-002-0442-9","volume":"95","author":"LRT T\u00e9bou","year":"2003","unstructured":"T\u00e9bou, L.RT., Zuazua, E.: Uniform exponential long time decay for the space semi-discretization of a locally damped wave equation via an artificial numerical viscosity. Numer. Math. 95(3), 563\u2013598 (2003)","journal-title":"Numer. Math."},{"issue":"1\u20133","key":"9320_CR35","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s10444-004-7629-9","volume":"26","author":"LT Tebou","year":"2007","unstructured":"Tebou, L.T., Zuazua, E.: Uniform boundary stabilization of the finite difference space discretization of the 1-d wave equation. Adv. Comput. Math. 26(1\u20133), 337\u2013365 (2007)","journal-title":"Adv. Comput. Math."},{"key":"9320_CR36","volume-title":"Observation and control for operator semigroups. In: Birkh\u00e4user Advanced Texts: Basler Lehrb\u00fccher [Birkh\u00e4user Advanced Texts: Basel Textbooks]","author":"M Tucsnak","year":"2009","unstructured":"Tucsnak, M., Weiss, G.: Observation and control for operator semigroups. In: Birkh\u00e4user Advanced Texts: Basler Lehrb\u00fccher [Birkh\u00e4user Advanced Texts: Basel Textbooks]. Birkh\u00e4user Verlag, Basel (2009)"},{"issue":"2","key":"9320_CR37","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1137\/S0036144503432862","volume":"47","author":"E Zuazua","year":"2005","unstructured":"Zuazua, E.: Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47(2), 197\u2013243 (2005) (electronic)","journal-title":"SIAM Rev."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9320-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-013-9320-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9320-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T06:59:52Z","timestamp":1563951592000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-013-9320-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,20]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["9320"],"URL":"https:\/\/doi.org\/10.1007\/s10444-013-9320-5","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,20]]}}}