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2000 | 27 | 2 | 239-250
Tytuł artykułu

On an optimal control problem for a quasilinear parabolic equation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
Rocznik
Tom
27
Numer
2
Strony
239-250
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-29
poprawiono
1999-10-11
Twórcy
autor
  • Mathematics Department, Faculty of Science,Minia University, Minia, Egypt
autor
  • Mathematics Department, Faculty of EducationP.O. Box 14, Ibri 516, Sultanate of Oman
Bibliografia
  • [1] M. Bergounioux and F. Tröltzsch, Optimality conditions and generalized bang-bang principle for a state constrained semilinear parabolic problem, Numer. Funct. Anal. Optim. 17 (1996), 517-536.
  • [2] P. Enidr, Optimal Control and Calculus of Variations, Oxford Sci. Publ., London, 1993.
  • [3] M. H. Farag, Application of the exterior penalty method for solving constrained optimal control problem, Math. Phys. Soc. Egypt, 1995.
  • [4] M. Goebel, On existence of optimal control, Math. Nachr. 93 (1979), 67-73.
  • [5] W. Krabs, Optimization and Approximation, Wiley, New York, 1979.
  • [6] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Parabolic Equations, Nauka, Moscow, 1976 (in Russian).
  • [7] O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics, Nau- ka, Moscow, 1973 (in Russian).
  • [8] J.-L. Lions, Optimal Control by Systems Described by Partial Differential Equations, Mir, Moscow, 1972 (in Russian).
  • [9] K. A. Lourie, Optimal Control in Problems of Mathematical Physics, Nauka, Moscow, 1975 (in Russian).
  • [10] V. P. Mikhailov, Partial Differential Equations, Nauka, Moscow, 1983 (in Russian).
  • [11] J. P. Raymond, Nonlinear boundary control semilinear parabolic equations with pointwise state constraints, Discrete Contin. Dynam. Systems 3 (1997), 341-370.
  • [12] J. P. Raymond and F. Tröltzsch, Second order sufficient optimality conditions for nonlinear parabolic control problems with constraints, preprint, Fak. Math., Tech. Univ. Chemnitz, 1998.
  • [13] A. N. Tikhonov and N. Ya. Arsenin, Methods for the Solution of Ill-Posed Problems, Nauka, Moscow, 1974 (in Russian).
  • [14] F. Tröltzsch, On the Lagrange-Newton-SQP method for the optimal control for semilinear parabolic equations, preprint, Fak. Math., Tech. Univ. Chemnitz, 1998.
  • [15] T. Tsachev, Optimal control of linear parabolic equation$:$ The constrained right-hand side as control function, Numer. Funct. Anal. Optim. 13 (1992), 369-380.
  • [16] A.-Q. Xing, The exact penalty function method in constrained optimal control problems, J. Math. Anal. Appl. 186 (1994), 514-522.
Typ dokumentu
Bibliografia
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