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Energy decay estimates for some weakly coupled Euler-Bernoulli and wave equations with indirect damping mechanisms
Pontryagin's principle for local solutions of optimal control governed by the 2D Navier-Stokes equations with mixed control-state constraints
1. | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China, China |
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show all references
References:
[1] |
2nd edition, North-Holland, Amsterdam, 1979. Google Scholar |
[2] |
Dimensional System," Birkhäuser, Boston, 1995. Google Scholar |
[3] |
Nonlinear Anal., 51 (2002), 509-536.
doi: 10.1016/S0362-546X(01)00843-4. |
[4] |
Nonlinear Anal., 52 (2003), 1911-1931.
doi: 10.1016/S0362-546X(02)00282-1. |
[5] |
Nonlinear Anal., 73 (2010), 3924-3939.
doi: 10.1016/j.na.2010.08.026. |
[6] |
SIAM J. Control Optim., 41 (2002), 583-606.
doi: 10.1137/S0363012901385769. |
[7] |
SIAM J. Control Optim., 39 (2000), 1182-1203. |
[8] |
SIAM J. Control Optim., 36 (1998), 1853-1879. Google Scholar |
[9] |
Math. Control Relat. Fields, 1 (2011), 267-306.
doi: 10.3934/mcrf.2011.1.267. |
[10] |
Math. Control Relat. Fields, 1 (2011), 189-230.
doi: 10.3934/mcrf.2011.1.189. |
[11] |
Systems Control Lett., 30 (1997), 93-100.
doi: 10.1016/S0167-6911(96)00083-7. |
[12] |
Math. Control Relat. Fields, 1 (2011), 307-330.
doi: 10.3934/mcrf.2011.1.307. |
[13] |
J. Inv. Ill-Posed Problems, 12 (2004), 43-123; Part II: $L_2(\Omega)$-estimates, J. Inv. Ill-Posed Problems, 12 (2004), 183-231, (MR2061430). |
[14] |
Math. Control Relat. Fields, 1 (2011), 149-175.
doi: 10.3934/mcrf.2011.1.149. |
[15] |
Math. Control Relat. Fields, 1 (2011), 177-187.
doi: 10.3934/mcrf.2011.1.177. |
[16] |
CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1983. Google Scholar |
[17] |
Proc. Roy. Soc. Edinburgh Sect. A, 124 (1994), 211-251.
doi: 10.1017/S0308210500028444. |
[18] |
in "Control and Estimation of Distributed Parameter Systems" (Vorau, 1996), Internat. Ser. Numer. Math., 126, Birkhäuser, Basel, (1998), 89-102. |
[19] |
Springer-Verlag, New York, 1983. Google Scholar |
[20] |
Nonlinear Anal., 31 (1998), 15-31.
doi: 10.1016/S0362-546X(96)00306-9. |
[21] |
SIAM J. Control Optim., 29 (1991), 895-908.
doi: 10.1137/0329049. |
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