Existence of optimal controls for viscous flow problems

A class of optimal control problems in viscous flow is studied. Main result is the existence theorem for optimal control. Three typical flow control problems are formulated within this general class.

[1]  Luciano de Simon.  Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine , 1964 .

[2]  H. O. Fattorini,et al.  Time-Optimal Control of Solutions of Operational Differenital Equations , 1964 .

[3]  川口 光年,et al.  O. A. Ladyzhenskaya: The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Sci. Pub. New York-London, 1963, 184頁, 15×23cm, 3,400円. , 1964 .

[4]  A. Balakrishnan.  Optimal Control Problems in Banach Spaces , 1965 .

[5]  Avner Friedman,et al.  Optimal control for parabolic equations. , 1967 .

[6]  A. G. Butkovskiĭ,et al.  Distributed control systems , 1969 .

[7]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[8]  J. Cooper.  SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONS , 1973 .

[9]  Hiroko Morimoto,et al.  On the Navier-Stokes initial value problem , 1974 .

[10]  増田 久弥.  On the Stability of Incompressible Viscous Fluid Motions Past Objects (非線形問題の解析 : Analysis of Nonlinear Problems, RIMS, 1974) , 1975 .

[11]  C. Amick.  Steady solutions of the Navier-Stokes equations in unbounded channels and pipes , 1977 .

[12]  D. Russell.  Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions , 1978 .

[13]  Kok Lay Teo,et al.  Optimal control of distributed parameter systems , 1981 .

[14]  Jacques-Louis Lions,et al.  Some Methods in the Mathematical Analysis of Systems and Their Control , 1981 .

[15]  Giuseppe Da Prato,et al.  Hamilton-Jacobi equations in Hilbert spaces , 1983 .

[16]  Adalbert Kerber,et al.  The Cauchy Problem , 1984 .

[17]  Jacques-Louis Lions,et al.  Control of distributed singular systems , 1985 .

[18]  Yoshikazu Giga,et al.  Domains of fractional powers of the Stokes operator in Lr spaces , 1985 .

[19]  V. Barbu.  Hamilton-Jacobi equations and nonlinear control problems , 1986 .

[20]  Jacques-Louis Lions.  Some Aspects of the Optimal Control of Distributed Parameter Systems , 1987 .

[21]  E. Barron,et al.  The necessary conditions for optimal control in Hilbert spaces , 1988 .

[22]  Daniel B. Henry.  Geometric Theory of Semilinear Parabolic Equations , 1989 .

[23]  Sri Sritharan,et al.  Invariant manifold theory for hydrodynamic transition , 1990 .

[24]  S. Sritharan.  An optimal control problem in exterior hydrodynamics , 1992, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[25]  Sri Sritharan,et al.  Necessary and sufficient conditions for optimal controls in viscous flow problems , 1994, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.