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Optimal controls of Boussinesq equations with state constraints. (English) Zbl 1100.49026
The paper considers an optimal control problem for a semilinear parabolic system (Boussinesq system) with controls in the right hand side of the equations, with Lipshitz continuous cost functional and with additional integral type state constraints. By means of a specialized penalty method necessary optimality conditions are obtained.

49K20 Optimality conditions for problems involving partial differential equations
35Q30 Navier-Stokes equations
Full Text: DOI
[1] Barbu, V., Optimal control of variational inequalities, () · Zbl 0574.49005
[2] Barbu, V., Analysis and control of nonlinear infinite dimensional systems, (1993), Academic Press Boston
[3] Barbu, V., Optimal control of navier – stokes equations with periodic inputs, Nonlinear anal., 31, 1, 15-31, (1998) · Zbl 0914.49009
[4] Constantin, P.; Foias, C., Navier – stokes equations, (1998), The University of Chicago Press Chicago
[5] Fattorini, H.O.; Sritharan, S.S., Necessary and sufficient conditions for optimal controls in viscous flow problems, Proc. roy. soc. Edinburgh sect. A, 124, 211-251, (1994) · Zbl 0800.49047
[6] Fursikov, A.V., Optimal control of distributed systemstheory and application, () · Zbl 0938.93003
[7] Li, X.; Yong, J., Necessary conditions for optimal control of distributed parameter system, SIAM J. control optim., 29, 895-908, (1991) · Zbl 0733.49025
[8] Li, X.; Yong, J., Optimal control theory for infinite dimensional systems, (1995), Birkhäuser Boston
[9] Lions, J.L.; Magenes, E., Non-homogeneous boundary valued problems and applications, (1972), Springer Berlin, Heidelberg, New York · Zbl 0223.35039
[10] Teman, R., Navier – stokes equations, (1979), North-Holland Amsterdam · Zbl 0406.35053
[11] Wang, G.S., Optimal control of parabolic differential equations with two point boundary state constraint, SIAM J. control optim., 38, 1639-1654, (2000) · Zbl 0963.49018
[12] Wang, G.S., Optimal control problem for parabolic variational inequalities, Acta math. sci. (China) B, 21, 4, 1-17, (2001)
[13] Wang, G.S., Optimal control of 3-dimensional navier – stokes equations with state constraints, SIAM J. control optim., 41, 2, 583-606, (2002) · Zbl 1022.93026
[14] Wang, G.S., Pontryagin maximum principle of optimal control governed by fluid dynamic systems with two point boundary state constraints, Nonlinear anal., 51, 3, 509-536, (2002) · Zbl 1013.49018
[15] Wang, G.S., Stabilization of the Boussinesq equation via internal feedback controls, Nonlinear anal., 52, 2, 485-506, (2003) · Zbl 1045.35055
[16] Wang, G.S.; Wang, L., Maximum principle for state-constrained optimal control of parabolic differential equations, Numer. funct. anal. optim., 1, 367-383, (2001)
[17] Wang, L.; Wang, G.S., Local internal controllability of the Boussinesq system, Nonlinear anal., 53, 5, 637-652, (2003) · Zbl 1071.35103
[18] Wang, G.S.; Wang, L., State-constrained optimal control governed by non-well-posed semilinear parabolic differential equation, SIAM J. control optim., 40, 5, 1517-1539, (2002) · Zbl 1013.49016
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