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2013 | 42 | nr 2 | 459--470
Tytuł artykułu

Optimal Control for a Steady State Dead Oil Isotherm Problem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of mechanics of a continuous medium. Existence and regularity results of the optimal control are proved, as well as necessary optimality conditions. (original abstract)
Rocznik
Tom
42
Numer
Strony
459--470
Opis fizyczny
Twórcy
  • Moulay Ismail University, Morocco
  • Bialystok University of Technology, Poland
  • University of Aveiro, Portugal
Bibliografia
  • BENSOUSSAN, A., LIONS, J.-L. and PAPANICOLAOU, G. (1978) Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications, 5, North-Holland, Amsterdam.
  • BODART, O., BOUREAU, A. V. and TOUZANI, R. (2001) Numerical investigation of optimal control of induction heating processes. Appl. Math. Modelling 25, 697-712.
  • FURSIKOV, A. V. (2000) Optimal Control of Distributed Systems. Theory and Applications, Translated from the 1999 Russian original by Tamara Rozhkovskaya. Translations of Mathematical Monographs, 187, Amer. Math. Soc., Providence, RI.
  • GAGNEUX, G. and MADAUNE-TORT, M. (1996) Analyse mathématique de modèles non linéaires de l'ingénierie pétrolière. Mathématiques & Applications (Berlin), 22, Springer, Berlin.
  • KOCH, H. and SOLONNIKOV, V. A. (2001) Lp-estimates for a solution to the nonstationary Stokes equations. J. Math. Sci. (New York) 106, 3, 3042-3072.
  • LADYZHENSKAYA, O. A., SOLONNIKOV, V. A. and URALTSEVA, N. N. (1967) Linear and Quasi-Linear Equations of Parabolic Type. Transl. Math. Monogr. 23, AMS, Providence, RI.
  • LEE, H.-C. and SHILKIN, T. (2005) Analysis of optimal control problems for the two-dimensional thermistor system. SIAM J. Control Optim. 44, 1, 268-282.
  • LIONS, J.-L. (1969) Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod.
  • LIONS, J.-L. (1971) Optimal Control of Systems Governed by Partial Differential Equations, Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, 170. Springer, New York.
  • MORDUKHOVICH, B. S. (2006) Variational Analysis and Generalized Differentiation. II. Grundlehren der Mathematischen Wissenschaften, 331, Springer, Berlin.
  • PESCH, H. J., RUND, A., VON WAHL, W. and WENDL, S. (2010) On some new phenomena in state-constrained optimal control if ODEs as well as PDEs are involved. Control Cybernet. 39, 3, 647-660.
  • RODRIGUES, J.-F. (1987) Obstacle Problems in Mathematical Physics. North-Holland Mathematics Studies, 134, North-Holland, Amsterdam.
  • ROUBIČEK, T. (2005) Nonlinear Partial Differential Equations with Applications. International Series of Numerical Mathematics, 153, Birkh¨auser, Basel.
  • SCHMIDT, S. and SCHULZ, V. (2010) Shape derivatives for general objective functions and the incompressible Navier-Stokes equations. Control Cybernet. 39, 3, 677-713.
  • SIDI AMMI, M. R. and TORRES, D. F. M. (2007a) Existence and regularity of optimal solution for a dead oil isotherm problem. Appl. Sci. 9, 5-12.
  • SIDI AMMI, M. R. and TORRES, D. F. M. (2007b) Necessary optimality conditions for a dead oil isotherm optimal control problem. J. Optim. Theory Appl. 135, 1, 135-143.
  • SIDI AMMI, M. R. and TORRES, D. F. M. (2008a) Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem. Math. Comput. Simulation 77, 2-3, 291-300.
  • SIDI AMMI, M. R. and TORRES, D. F. M. (2008b) Necessary optimality condition for a discrete dead oil isotherm optimal control problem. In: Mathematical Control Theory and Finance, 387-395, Springer, Berlin.
  • SOLONNIKOV, V. A. (1965) On boundary value problems for linear paraboli systems of differential equations of general form. Trudy Mat. Inst. Steklov. 83, 3-163.
  • XU, X. (1996) Local and global existence of continuous temperature in the electrical heating of conductors. Houston J. Math. 22, 2, 435-455.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171305143

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