-
Previous Article
Boundary stabilization of the Navier-Stokes equations with feedback controller via a Galerkin method
- EECT Home
- This Issue
-
Next Article
Recovery of time dependent volatility coefficient by linearization
Cross-like internal observability of rectangular membranes
1. | Département de mathématique, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg Cedex, France |
2. | Université Paris-Est, Cité Descartes-Champs-sur-Marne, 5, boulevard Descartes, 77454 Marne la Vallée, France |
References:
[1] |
C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), 1024-1065.
doi: 10.1137/0330055. |
[2] |
A. Haraux, Contrôlabilité exacte d'une membrane rectangulaire au moyen d'une fonctionnelle analytique localisée, C. R. Acad. Sci. Paris Sér. I Math., 306 (1988), 125-128. |
[3] |
A. Haraux, Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures Appl., 68 (1989), 457-465. |
[4] |
A. Haraux, On a completion problem in the theory of distributed control of wave equations, Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. X (Paris, 1987-1988), Pitman Res. Notes Math. Ser., Longman Sci. Tech., Harlow, 220 (1991), 241-271. |
[5] |
A. E. Ingham, Some trigonometrical inequalities with applications in the theory of series, Math. Z., 41 (1936), 367-379.
doi: 10.1007/BF01180426. |
[6] |
V. Komornik and P. Loreti, Fourier Series in Control Theory, Springer-Verlag, New York, 2005. |
[7] |
J.-L. Lions, Exact controllability, stabilizability, and perturbations for distributed systems, SIAM Rev., 30 (1988), 1-68.
doi: 10.1137/1030001. |
[8] |
J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. Contrôlabilité exacte, Masson, Paris, 1988. |
[9] |
P. Loreti and M. Mehrenberger, An Ingham type proof for a two-grid observability theorem, ESAIM Control Optim. Calc. Var., 14 (2008), 604-631.
doi: 10.1051/cocv:2007062. |
[10] |
P. Loreti and V. Valente, Partial exact controllability for spherical membranes, SIAM J. Control Optim., 35 (1997), 641-653.
doi: 10.1137/S036301299526962X. |
[11] |
M. Mehrenberger, An Ingham type proof for the boundary observability of a N-d wave equation, C. R. Math. Acad. Sci. Paris, 347 (2009), 63-68.
doi: 10.1016/j.crma.2008.11.002. |
[12] |
Y. Privat, E. Trélat and E. Zuazua, Optimal observation of the one-dimensional wave equation, J. Fourier Anal. Appl., 19 (2013), 514-544.
doi: 10.1007/s00041-013-9267-4. |
show all references
References:
[1] |
C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), 1024-1065.
doi: 10.1137/0330055. |
[2] |
A. Haraux, Contrôlabilité exacte d'une membrane rectangulaire au moyen d'une fonctionnelle analytique localisée, C. R. Acad. Sci. Paris Sér. I Math., 306 (1988), 125-128. |
[3] |
A. Haraux, Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures Appl., 68 (1989), 457-465. |
[4] |
A. Haraux, On a completion problem in the theory of distributed control of wave equations, Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. X (Paris, 1987-1988), Pitman Res. Notes Math. Ser., Longman Sci. Tech., Harlow, 220 (1991), 241-271. |
[5] |
A. E. Ingham, Some trigonometrical inequalities with applications in the theory of series, Math. Z., 41 (1936), 367-379.
doi: 10.1007/BF01180426. |
[6] |
V. Komornik and P. Loreti, Fourier Series in Control Theory, Springer-Verlag, New York, 2005. |
[7] |
J.-L. Lions, Exact controllability, stabilizability, and perturbations for distributed systems, SIAM Rev., 30 (1988), 1-68.
doi: 10.1137/1030001. |
[8] |
J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. Contrôlabilité exacte, Masson, Paris, 1988. |
[9] |
P. Loreti and M. Mehrenberger, An Ingham type proof for a two-grid observability theorem, ESAIM Control Optim. Calc. Var., 14 (2008), 604-631.
doi: 10.1051/cocv:2007062. |
[10] |
P. Loreti and V. Valente, Partial exact controllability for spherical membranes, SIAM J. Control Optim., 35 (1997), 641-653.
doi: 10.1137/S036301299526962X. |
[11] |
M. Mehrenberger, An Ingham type proof for the boundary observability of a N-d wave equation, C. R. Math. Acad. Sci. Paris, 347 (2009), 63-68.
doi: 10.1016/j.crma.2008.11.002. |
[12] |
Y. Privat, E. Trélat and E. Zuazua, Optimal observation of the one-dimensional wave equation, J. Fourier Anal. Appl., 19 (2013), 514-544.
doi: 10.1007/s00041-013-9267-4. |
[1] |
Vilmos Komornik, Gérald Tenenbaum. An Ingham--Müntz type theorem and simultaneous observation problems. Evolution Equations and Control Theory, 2015, 4 (3) : 297-314. doi: 10.3934/eect.2015.4.297 |
[2] |
Michel Potier-Ferry, Foudil Mohri, Fan Xu, Noureddine Damil, Bouazza Braikat, Khadija Mhada, Heng Hu, Qun Huang, Saeid Nezamabadi. Cellular instabilities analyzed by multi-scale Fourier series: A review. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 585-597. doi: 10.3934/dcdss.2016013 |
[3] |
Ferenc Weisz. Cesàro summability and Lebesgue points of higher dimensional Fourier series. Mathematical Foundations of Computing, 2022, 5 (3) : 241-257. doi: 10.3934/mfc.2021033 |
[4] |
Giovanni Cupini, Eugenio Vecchi. Faber-Krahn and Lieb-type inequalities for the composite membrane problem. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2679-2691. doi: 10.3934/cpaa.2019119 |
[5] |
Ali Gholami, Mauricio D. Sacchi. Time-invariant radon transform by generalized Fourier slice theorem. Inverse Problems and Imaging, 2017, 11 (3) : 501-519. doi: 10.3934/ipi.2017023 |
[6] |
Dezhong Chen, Li Ma. A Liouville type Theorem for an integral system. Communications on Pure and Applied Analysis, 2006, 5 (4) : 855-859. doi: 10.3934/cpaa.2006.5.855 |
[7] |
Abdon E. Choque-Rivero, Iván Area. A Favard type theorem for Hurwitz polynomials. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 529-544. doi: 10.3934/dcdsb.2019252 |
[8] |
Michael Ruzhansky, Jens Wirth. Dispersive type estimates for fourier integrals and applications to hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 1263-1270. doi: 10.3934/proc.2011.2011.1263 |
[9] |
Albert Fathi. An Urysohn-type theorem under a dynamical constraint. Journal of Modern Dynamics, 2016, 10: 331-338. doi: 10.3934/jmd.2016.10.331 |
[10] |
Hiroshi Isozaki, Hisashi Morioka. A Rellich type theorem for discrete Schrödinger operators. Inverse Problems and Imaging, 2014, 8 (2) : 475-489. doi: 10.3934/ipi.2014.8.475 |
[11] |
Xinjing Wang. Liouville type theorem for Fractional Laplacian system. Communications on Pure and Applied Analysis, 2020, 19 (11) : 5253-5268. doi: 10.3934/cpaa.2020236 |
[12] |
Anh Tuan Duong, Quoc Hung Phan. A Liouville-type theorem for cooperative parabolic systems. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 823-833. doi: 10.3934/dcds.2018035 |
[13] |
Shigeru Sakaguchi. A Liouville-type theorem for some Weingarten hypersurfaces. Discrete and Continuous Dynamical Systems - S, 2011, 4 (4) : 887-895. doi: 10.3934/dcdss.2011.4.887 |
[14] |
Zhi Liu, Tie Zhang. An improved ARMA(1, 1) type fuzzy time series applied in predicting disordering. Numerical Algebra, Control and Optimization, 2020, 10 (3) : 355-366. doi: 10.3934/naco.2020007 |
[15] |
Xiaohui Yu. Liouville type theorem for nonlinear elliptic equation with general nonlinearity. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4947-4966. doi: 10.3934/dcds.2014.34.4947 |
[16] |
Xinjing Wang, Pengcheng Niu, Xuewei Cui. A Liouville type theorem to an extension problem relating to the Heisenberg group. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2379-2394. doi: 10.3934/cpaa.2018113 |
[17] |
Simão P. S. Santos, Natália Martins, Delfim F. M. Torres. Noether's theorem for higher-order variational problems of Herglotz type. Conference Publications, 2015, 2015 (special) : 990-999. doi: 10.3934/proc.2015.990 |
[18] |
Weiwei Zhao, Jinge Yang, Sining Zheng. Liouville type theorem to an integral system in the half-space. Communications on Pure and Applied Analysis, 2014, 13 (2) : 511-525. doi: 10.3934/cpaa.2014.13.511 |
[19] |
Yufeng Shi, Qingfeng Zhu. A Kneser-type theorem for backward doubly stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1565-1579. doi: 10.3934/dcdsb.2010.14.1565 |
[20] |
Xiaojun Huang, Yuan Lian, Changrong Zhu. A Billingsley-type theorem for the pressure of an action of an amenable group. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 959-993. doi: 10.3934/dcds.2019040 |
2020 Impact Factor: 1.081
Tools
Metrics
Other articles
by authors
[Back to Top]