×
Lasiecka, Irena

State constrained control problems for parabolic systems: Regularity of optimal solutions. (English) Zbl 0431.49015

Appl. Math. Optimization 6, 1-29 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0431.49015

Cited in 13 Documents

MSC:

49K20 Optimality conditions for problems involving partial differential equations
49K40 Sensitivity, stability, well-posedness
35B37 PDE in connection with control problems (MSC2000)
35K99 Parabolic equations and parabolic systems
49M15 Newton-type methods
35B65 Smoothness and regularity of solutions to PDEs
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

quadratic control problem; smoothness of optimal control; error estimating; approximation
Cite Review PDF
Full Text: DOI

References:

[1] J. Aubin, Approximation of Elliptic Boundary Value Problems, Wiley-Interscience, New York, 1972. · Zbl 0248.65063
[2] A. V. Balakrishnan, Applied Functional Analysis, Springer-Verlag, 1976. · Zbl 0333.93051
[3] V. Barbu, Constrained control problems with convex cost in Hilbert space,J. of Math Analysis 56, 529-547, 1976. · Zbl 0342.42008 · doi:10.1016/0022-247X(76)90023-8
[4] W. Borsage and McKnight, The Ritz Galerkin procedure for parabolic control problems,SIAM J. on Control, 11, 510-524, 1973. · doi:10.1137/0311040
[5] N. Dunford and Y. Schwartz, Linear Operators,Interscience, 1, New York, 1958.
[6] A. Friedman,Partial Differential Equations, Holt, Rinehart and Winston, Inc., New York, 1965. · Zbl 0192.19601
[7] D. Fujiwara, Concrete Characterization of the Domains of Fractional Powers of some Elliptic Differential Operators of the Second Order,Proc. Japan Acad., 43, 82-86, 1967. · Zbl 0154.16201 · doi:10.3792/pja/1195521686
[8] I. Gelfand and S. Fomin, Calculus of Variations, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1965. · Zbl 0127.05402
[9] W. Hager, Lipschitz continuity for constrained processes,SIAM J. on Control and Optimization, to appear. · Zbl 0426.90083
[10] W. Hager, The Ritz-Trefftz method for state and control constrained optimal control problems,SIAM J. on Numerical Analysis, 12, 854-867, 1975. · Zbl 0322.49021 · doi:10.1137/0712063
[11] W. Hager and S. Mitter, Lagrange duality for the convex control problems,SIAM J. on Control, 14, 843-456, 1976. · Zbl 0336.49007 · doi:10.1137/0314054
[12] E. Hille and R. Phillips: Functional Analysis and Semigroups, American Mathematical Society, Providence, Rhode Island, 1957. · Zbl 0078.10004
[13] S. Kurcyusz, On the existence and nonexistence of Lagrange’s multipliers in Banach spaces.IOTA 20, 1, 1976. · Zbl 0309.49010
[14] I. Lasiecka and K. Malanowski, On regularity of solutions to convex optimal control problems with control constraints for parabolic systems,Control and Cybernetics, 6, 57-74, 1977. · Zbl 0365.49003
[15] J. Lions, Control Optimal des Systemes Gouvernes par des Equations aux Derivees Partielles. Dunod, Paris, 1968.
[16] J. Lions and E. Magenes,Problemes aux Limites Nonhomogenes, 2. Dunod, Paris, 1968. · Zbl 0165.10801
[17] W. Rudin,Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1964. · Zbl 0148.02903
[18] R. Sikorski, Advanced Calculus Functions of Several Variables, PWN, Warsaw, 1969. · Zbl 0182.37901
[19] J. Sokolowski, On parametric optimal control for weak solutions of abstract linear parabolic equations. Ph.D. Dissertation, Institute of Organization and Management, Warsaw, 1975. · Zbl 0319.49012
[20] L. De Simon, Un’applicazione della teoria degli integrali sigolari allo studio delle equazioni differenziali lineari astratte del primo ordine.Rendiconti del Seminario Mathematico della Universite di Padova, 34, 205-223, 1964. · Zbl 0196.44803
[21] D. Washburn, A semigroup approach to time optimal boundary control of diffusion processes, Ph.D. Dissertation, UCLA, 1974. · Zbl 0284.60092
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.