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Control of a Korteweg-de Vries equation: A tutorial
1. | Departamento de Matemática, Universidad Técnica Federico Santa María, Avda. España 1680, Casilla 110-V, Valparaíso, Chile |
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L. Baudouin, E. Cerpa, E. Crépeau and A. Mercado, On the determination of the principal coefficient from boundary measurements in a KdV equation,, J. Inverse Ill-Posed Probl., ().
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Internat. J. Control, 74 (2001), 1096-1106.
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Ph.D thesis, Université Paris-Sud, Paris, 2002. Google Scholar |
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Differential Integral Equations, 20 (2007), 601-642. |
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Asymptot. Anal., 60 (2008), 61-100. |
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Systems Control Lett., 59 (2010), 390-395.
doi: 10.1016/j.sysconle.2010.05.001. |
[26] |
Math. Res. Lett., 10 (2003), 833-846.
doi: 10.4310/MRL.2003.v10.n6.a10. |
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Philos. Mag., 39 (1895), 422-443.
doi: 10.1080/14786449508620739. |
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Advances in Design and Control, 16, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2008. |
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ESAIM Control Optim. Calc. Var., 11 (2005), 473-486.
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ESAIM Control Optim. Calc. Var., 2 (1997), 33-55.
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ESAIM Control Optim. Calc. Var., 10 (2004), 346-380.
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[38] |
SIAM J. Control Optim., 45 (2006), 927-956.
doi: 10.1137/050631409. |
[39] |
J. Syst. Sci. Complex., 22 (2009), 647-682.
doi: 10.1007/s11424-009-9194-2. |
[40] |
SIAM Rev., 20 (1978), 639-739.
doi: 10.1137/1020095. |
[41] |
SIAM J. Control Optim., 31 (1993), 659-676.
doi: 10.1137/0331030. |
[42] |
J. Math. Anal. Appl., 190 (1995), 449-488.
doi: 10.1006/jmaa.1995.1087. |
[43] |
J. Differential Equations, 66 (1987), 118-139.
doi: 10.1016/0022-0396(87)90043-X. |
[44] |
Ann. Mat. Pura Appl. (4), 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
[45] |
SIAM J. Control Optim., 34 (1996), 892-912.
doi: 10.1137/S0363012994269491. |
[46] |
CBMS Regional Conference Series in Mathematics, 106, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006. |
[47] |
SIAM J. Control Optim., 43 (2005), 2233-2244.
doi: 10.1137/S0363012901388452. |
[48] |
Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. |
[49] |
SIAM J. Math. Anal., 23 (1992), 55-71.
doi: 10.1137/0523004. |
[50] |
SIAM J. Control Optim., 37 (1999), 543-565.
doi: 10.1137/S0363012997327501. |
show all references
References:
[1] |
SIAM J. Control Optim., 30 (1992), 1024-1065.
doi: 10.1137/0330055. |
[2] |
L. Baudouin, E. Cerpa, E. Crépeau and A. Mercado, On the determination of the principal coefficient from boundary measurements in a KdV equation,, J. Inverse Ill-Posed Probl., ().
doi: 10.1515/jip-2013-0015. |
[3] |
J. Math. Pures Appl. (9), 84 (2005), 851-956.
doi: 10.1016/j.matpur.2005.02.005. |
[4] |
J. Funct. Anal., 232 (2006), 328-389.
doi: 10.1016/j.jfa.2005.03.021. |
[5] |
SIAM J. Math. Anal., 14 (1983), 1056-1106.
doi: 10.1137/0514085. |
[6] |
Collection Mathématiques Appliquées pour la Maîtrise [Collection of Applied Mathematics for the Master's Degree], Masson, Paris, 1983. |
[7] |
SIAM J. Control Optim., 46 (2007), 877-899.
doi: 10.1137/06065369X. |
[8] |
IEEE Trans. Automat. Control, 58 (2013), 1688-1695.
doi: 10.1109/TAC.2013.2241479. |
[9] |
Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 457-475.
doi: 10.1016/j.anihpc.2007.11.003. |
[10] |
Discrete Contin. Dyn. Syst. Ser. B, 11 (2009), 655-668.
doi: 10.3934/dcdsb.2009.11.655. |
[11] |
SIAM J. Control Optim., 51 (2013), 2976-3010.
doi: 10.1137/120891721. |
[12] |
Comm. in Contemp. Math., 11 (2009), 495-521.
doi: 10.1142/S0219199709003454. |
[13] |
Math. Control Signal Systems, 5 (1992), 295-312.
doi: 10.1007/BF01211563. |
[14] |
J. Math. Pures Appl. (9), 75 (1996), 155-188. |
[15] |
ESAIM Control Optim. Calc. Var., 8 (2002), 513-554.
doi: 10.1051/cocv:2002050. |
[16] |
C. R. Acad. Sci. Paris, 342 (2006), 103-108.
doi: 10.1016/j.crma.2005.11.004. |
[17] |
Mathematical Surveys and Monographs, 136, American Mathematical Society, Providence, RI, 2007. |
[18] |
J. Eur. Math. Soc., 6 (2004), 367-398. |
[19] |
SIAM J. Control Optim., 43 (2004), 549-569.
doi: 10.1137/S036301290342471X. |
[20] |
Internat. J. Control, 74 (2001), 1096-1106.
doi: 10.1080/00207170110052202. |
[21] |
Ph.D thesis, Université Paris-Sud, Paris, 2002. Google Scholar |
[22] |
J. Funct. Anal., 244 (2007), 504-535.
doi: 10.1016/j.jfa.2006.11.004. |
[23] |
Differential Integral Equations, 20 (2007), 601-642. |
[24] |
Asymptot. Anal., 60 (2008), 61-100. |
[25] |
Systems Control Lett., 59 (2010), 390-395.
doi: 10.1016/j.sysconle.2010.05.001. |
[26] |
Math. Res. Lett., 10 (2003), 833-846.
doi: 10.4310/MRL.2003.v10.n6.a10. |
[27] |
Philos. Mag., 39 (1895), 422-443.
doi: 10.1080/14786449508620739. |
[28] |
Advances in Design and Control, 16, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2008. |
[29] |
Proc. Amer. Math. Soc., 135 (2007), 1515-1522.
doi: 10.1090/S0002-9939-07-08810-7. |
[30] |
Universitext, Springer, New York, 2009. |
[31] |
Recherches en Mathématiques Appliquées, 9, Masson, Paris, 1988. |
[32] |
Math. Methods Appl. Sci., 30 (2007), 1419-1435.
doi: 10.1002/mma.847. |
[33] |
ESAIM Control Optim. Calc. Var., 11 (2005), 473-486.
doi: 10.1051/cocv:2005015. |
[34] |
Applied Mathematical Sciences, 44, Springer, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[35] |
Quart. Appl. Math., 60 (2002), 111-129. |
[36] |
ESAIM Control Optim. Calc. Var., 2 (1997), 33-55.
doi: 10.1051/cocv:1997102. |
[37] |
ESAIM Control Optim. Calc. Var., 10 (2004), 346-380.
doi: 10.1051/cocv:2004012. |
[38] |
SIAM J. Control Optim., 45 (2006), 927-956.
doi: 10.1137/050631409. |
[39] |
J. Syst. Sci. Complex., 22 (2009), 647-682.
doi: 10.1007/s11424-009-9194-2. |
[40] |
SIAM Rev., 20 (1978), 639-739.
doi: 10.1137/1020095. |
[41] |
SIAM J. Control Optim., 31 (1993), 659-676.
doi: 10.1137/0331030. |
[42] |
J. Math. Anal. Appl., 190 (1995), 449-488.
doi: 10.1006/jmaa.1995.1087. |
[43] |
J. Differential Equations, 66 (1987), 118-139.
doi: 10.1016/0022-0396(87)90043-X. |
[44] |
Ann. Mat. Pura Appl. (4), 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
[45] |
SIAM J. Control Optim., 34 (1996), 892-912.
doi: 10.1137/S0363012994269491. |
[46] |
CBMS Regional Conference Series in Mathematics, 106, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006. |
[47] |
SIAM J. Control Optim., 43 (2005), 2233-2244.
doi: 10.1137/S0363012901388452. |
[48] |
Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. |
[49] |
SIAM J. Math. Anal., 23 (1992), 55-71.
doi: 10.1137/0523004. |
[50] |
SIAM J. Control Optim., 37 (1999), 543-565.
doi: 10.1137/S0363012997327501. |
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