Abstract
A class of optimal control problems in viscous flow is studied. Main results are the Pontryagin maximum principle and the verification theorem for the Hamilton-Jacobi-Bellman equation.
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References
V. Barbu, Hamilton-Jacobi equations and nonlinear control problems, J. of Math. Anlysis and applications 120 (1986), 494–509.
V. Barbu and E.N. Barron and R. Jensen, Necessary conditions for optimal control in Hilbert spaces, J. of Math. Anlysis and applications 133 (1988), 151–162.
V. Barbu and G. Da Prato, Hamilton-Jacobi equations in Hilbert spaces, Pitman, Boston, 1983.
E.N. Barron and R. Jensen, Pontryagin maximum principle from dynamic programming and viscosity solutions to first order partial differential equations, Trans. Amer. Math. Soc. 298 (1986), 635–641.
F. Clarke, Optimization and Nonsmooth Analysis, Wiley — Interscience, New York, 1983.
F. Clarke, Methods of dynamic and nonsmooth optimization, SIAM-CBMS-NSF, Philadelphia, 1989.
M.G. Crandall and L.C. Evans and P.L. Lions, Some properties of the viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282 (2) (1984), 487–502.
M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1) (1983), 1–42.
R.J. Elliott, Viscosity solutions and optimal control, Longman Publishers, Essex, 1987.
H. Fattorini and S.S. Sritharan, Optimal control theory of viscous flow problems, To be published, 1990.
H. Frankowska, Hamilton-Jacobi equation: viscosity solutions and generalized gradients, Journal of Mathematical Anal. Applications 141 (1989), 21–26.
S.S. Sritharan, Invariant Manifold Theory For Hydrodynamic Transition, John Wiley, New York, 1990.
S.S. Sritharan, An Optimal Control Problem In Exterior Hydrodynamics, New Trends And Applications Of Distributed Parameter Control Systems (G. Chen, L. Markus, E.B. Lee and W. Littman, eds.), Marcel Dekker, 1990.
R. Temam, Navier-Stokes Equations, third edition, North-Holland Publ. Comp., Amsterdam, 1984.
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© 1991 Springer Basel AG
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Sritharan, S.S. (1991). Dynamic programming of the Navier-Stokes equations. In: Desch, W., Kappel, F., Kunisch, K. (eds) Estimation and Control of Distributed Parameter Systems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 100. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6418-3_21
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DOI: https://doi.org/10.1007/978-3-0348-6418-3_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2676-0
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