Abstract
Approximation properties of pseudo-parabolic optimal controls to the parabolic optimal control are considered for two concrete problems.
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References
Avner Friedman,Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs, N. J., 1965.
O. A. Ladyzhenskaya, and N. N. Ural'tseva,Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968.
J. Lagnese, Approximation of solutions of differential equations in Hilbert space,J. Math. Soc. Japan, 25, 132–143 (1973).
J. L. Lions, and E. Magenes,Non-Homogeneous Boundary Value Problems and Applications, I and II, transl. by P. Kenneth, Springer-Verlag, New York, 1972.
J. L. Lions,Optimal Control of Systems Governed by Partial Differential Equations, transl. by S. K. Mitter, Springer-Verlag, New York, 1971.
D. G. Luenberger,Optimization by Vector Space Methods, Wiley, New York, 1969.
R. E. Showalter, and T. W. Ting, Pseudo-parabolic partial differential equations,SIAM J. Math. Anal., 1, 1–26 (1970).
R. E. Showalter, Regularization and approximation of second order evolution equations,SIAM J. Math. Anal., 7, 461–472 (1976).
T. W. Ting, Parabolic and pseudo-parabolic partial differential equations,J. Math. Soc. Japan, 21, 440–453 (1969).
L. W. White, Control problems governed by pseudo-parabolic partial differential equations,Trans. Am. Math. Soc., 250, 235–246 (1979).
L. W. White, Control of a pseudo-parabolic initial-value problem to a target function,SIAM J. Control, 17, 587–595 (1979).
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Communicated by W. Fleming
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White, L.W. Convergence properties of optimal controls of pseudo-parabolic problems. Appl Math Optim 7, 141–147 (1981). https://doi.org/10.1007/BF01442112
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DOI: https://doi.org/10.1007/BF01442112