@article{SLSEDP_2015-2016____A7_0,
author = {Alazard, Thomas},
title = {Controllability and stabilization of water waves},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:7},
pages = {1--17},
publisher = {Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique},
year = {2015-2016},
doi = {10.5802/slsedp.96},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.96/}
}
TY - JOUR AU - Alazard, Thomas TI - Controllability and stabilization of water waves JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:7 PY - 2015-2016 SP - 1 EP - 17 PB - Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.96/ DO - 10.5802/slsedp.96 LA - en ID - SLSEDP_2015-2016____A7_0 ER -
%0 Journal Article %A Alazard, Thomas %T Controllability and stabilization of water waves %J Séminaire Laurent Schwartz — EDP et applications %Z talk:7 %D 2015-2016 %P 1-17 %I Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.96/ %R 10.5802/slsedp.96 %G en %F SLSEDP_2015-2016____A7_0
Alazard, Thomas. Controllability and stabilization of water waves. Séminaire Laurent Schwartz — EDP et applications (2015-2016), Exposé no. 7, 17 p. doi : 10.5802/slsedp.96. http://www.numdam.org/articles/10.5802/slsedp.96/
[1] Fatiha Alabau-Boussouira, Roger Brockett, Olivier Glass, Jérôme Le Rousseau, and Enrique Zuazua. Control of partial differential equations, volume 2048 of Lecture Notes in Mathematics. Springer, Heidelberg; Fondazione C.I.M.E., Florence, 2012.
[2] Thomas Alazard. Boundary observability of gravity water waves. 2015. | arXiv
[3] Thomas Alazard. Stabilization of gravity water waves. 2016. | arXiv
[4] Thomas Alazard and Pietro Baldi. Gravity capillary standing water waves. Arch. Ration. Mech. Anal., 217(3):741–830, 2015.
[5] Thomas Alazard, Pietro Baldi, and Daniel Han-Kwan. Control of water waves. J. Eur. Math. Soc. (JEMS), to appear. | arXiv
[6] Thomas Alazard, Nicolas Burq, and Claude Zuily. On the water-wave equations with surface tension. Duke Math. J., 158(3):413–499, 2011.
[7] Thomas Alazard, Nicolas Burq and Claude Zuily. Cauchy theory for the gravity water waves system with non localized initial data. Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear, . | arXiv
[8] Thomas Alazard, Nicolas Burq, and Claude Zuily. The water-wave equations: from Zakharov to Euler. In Studies in phase space analysis with applications to PDEs, volume 84 of Progr. Nonlinear Differential Equations Appl., pages 1–20. Birkhäuser/Springer, New York, 2013.
[9] Thomas Alazard and Guy Métivier. Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Comm. Partial Differential Equations, 34(10-12):1632–1704, 2009.
[10] Pietro Baldi, Emanuele Haus. A Nash-Moser-Hörmander implicit function theorem with applications to control and Cauchy problems for PDEs. | arXiv
[11] Joseph Boussinesq. Sur une importante simplification de la théorie des ondes que produisent, à la surface d’un liquide, l’emersion d’un solide ou l’impulsion d’un coup de vent. Ann. Sci. École Norm. Sup. (3), 27:9–42, 1910.
[12] T. Brooke Benjamin and Peter J. Olver. Hamiltonian structure, symmetries and conservation laws for water waves. J. Fluid Mech., 125:137–185, 1982.
[13] Umberto Biccari. Internal control for non-local Schrödinger and wave equations involving the fractional Laplace operator. | arXiv
[14] Félicien Bonnefoy. Experimental and numerical modelling of severe sea states. PhD thesis, Université de Nantes, March 2005.
[15] Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, and Javier Gómez-Serrano. Finite time singularities for the free boundary incompressible Euler equations. Ann. of Math. (2), 178(3):1061–1134, 2013.
[16] Didier Clamond, Dorian Fructus, John Grue, and Øyvind Kristiansen. An efficient model for three-dimensional surface wave simulations. II. Generation and absorption. J. Comput. Phys., 205(2):686–705, 2005.
[17] Alain Clément. Benchmark test cases for Numerical Wave Absorption. Report on the 1st Workshop of ISOPE Numerical Wave Tank group;Montreal 1998. In 9th Int. Offshore and Polar Engineering Conf. ISOPE’ 99, Brest, France, 1999.
[18] Jean-Michel Coron. Control and nonlinearity, volume 136 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2007.
[19] Daniel Coutand and Steve Shkoller. On the finite-time splash and splat singularities for the 3-D free-surface Euler equations. Comm. Math. Phys., 325(1):143–183, 2014.
[20] Walter Craig. An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits. Comm. Partial Differential Equations, 10(8):787–1003, 1985.
[21] Walter Craig and Catherine Sulem. Numerical simulation of gravity waves. J. Comput. Phys., 108(1):73–83, 1993.
[22] Belhassen Dehman and Gilles Lebeau. Analysis of the HUM control operator and exact controllability for semilinear waves in uniform time. SIAM J. Control Optim. 48 (2009), no. 2, 521–550.
[23] Belhassen Dehman, Gilles Lebeau, and Enrique Zuazua. Stabilization and control for the subcritical semilinear wave equation. Annales scientifiques de l’École Normale Supérieure, 36(4):525–551, 2003.
[24] Gaelle Duclos, Alain Clément, and Gontran Chatry. Absorption of outgoing waves in a numerical wave tank using a self-adaptive boundary condition. International Journal of Offshore and Polar Engineering, 11(03), 2001.
[25] Guillaume Ducrozet. Modelisation of nonlinear processes in generation and propagation of sea states with a spectral approach. PhD thesis, Université de Nantes ; Ecole Centrale de Nantes (ECN), November 2007.
[26] Stéphan T Grilli and Juan Horrillo. Numerical generation and absorption of fully nonlinear periodic waves. Journal of Engineering Mechanics, 123(10):1060–1069, 1997.
[27] Moshe Israeli and Steven A. Orszag. Approximation of radiation boundary conditions. J. Comput. Phys., 41(1):115 – 135, 1981.
[28] G. I. Jennings, D. Prigge, S. Carney, S. Karni, J. B. Rauch, and R. Abgrall. Water wave propagation in unbounded domains. part II: Numerical methods for fractional pdes. Journal of Computational Physics, 275:443–458, 10 2014.
[29] Geri I. Jennings, Smadar Karni, and Jeffrey Rauch. Water wave propagation in unbounded domains. Part I: nonreflecting boundaries. J. Comput. Phys., 276:729–739, 2014.
[30] Jean-Pierre Kahane. Pseudo-périodicité et séries de Fourier lacunaires. Ann. Sci. École Norm. Sup., 79 (1962), 93-150.
[31] David Lannes. Well-posedness of the water-waves equations. J. Amer. Math. Soc., 18(3):605–654 (electronic), 2005.
[32] Camille Laurent. Global controllability and stabilization for the nonlinear Schrödinger equation on an interval. ESAIM-COCV, 16(2): 356–379, 2010.
[33] Jacques-Louis Lions. Exact controllability, stabilization and perturbations for distributed systems. SIAM Rev., 30(1):1–68, 1988.
[34] Pierre Lissy. On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension. SIAM J. Control Optim., 52(4):2651–2676, 2014.
[35] Elaine Machtyngier and Enrique Zuazua. Stabilization of the Schrödinger equation. Portugal. Math., 51(2):243–256, 1994.
[36] Bernard Le Méhauté. Progressive wave absorber. Journal of Hydraulic Research, 10(2):153–169, 1972.
[37] Benoît Mésognon-Gireau. The Cauchy problem on large time for the Water Waves equations with large topography variations. | arXiv
[38] Luc Miller. Resolvent conditions for the control of unitary groups and their approximations. J. Spectr. Theory, 2(1):1–55, 2012.
[39] Russell M. Reid. Open loop control of water waves in an irregular domain. SIAM J. Control Optim., 24(4):789–796, 1986.
[40] Russell M. Reid. Control time for gravity-capillary waves on water. SIAM J. Control Optim., 33(5):1577–1586, 1995.
[41] Russell M. Reid and David L. Russell. Boundary control and stability of linear water waves. SIAM J. Control Optim., 23(1):111–121, 1985.
[42] Lionel Rosier. Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain. ESAIM Control Optim. Calc. Var., 2:33–55 (electronic), 1997.
[43] Semyon V. Tsynkov. Numerical solution of problems on unbounded domains. A review. Appl. Numer. Math., 27(4):465–532, 1998. Absorbing boundary conditions.
[44] Vladimir E. Zakharov. Stability of periodic waves of finite amplitude on the surface of a deep fluid. Journal of Applied Mechanics and Technical Physics, 9(2):190–194, 1968.
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