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Abstrakty
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 optima control are proved, as well as necessary optimality conditions.
Czasopismo
Rocznik
Tom
Strony
459--470
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Department of Mathematics, AMNEA Group, Faculty of Sciences and Techniques, Moulay Ismail University, B.P. 509 Errachidia, Morocco
autor
- Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok, Poland
autor
- CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Bibliografia
- 1. BENSOUSSAN, A., LIONS, J.-L. and PAPANICOLAOU, G. (1978) Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications, 5, North-Holland, Amsterdam.
- 2. BODART, O., BOUREAU, A. V. and TOUZANI, R. (2001) Numerical investigation of optimal control of induction heating processes. Appl. Math. Modelling 25, 697–712.
- 3. 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.
- 4. GAGNEUX, G. and MADAUNE-TORT, M. (1996) Analyse mathématique de modèles non linéaires de l’ingénierie pétrolière. Mathématiques & Applications (Berlin), 22, Springer, Berlin.
- 5. 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.
- 6. 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.
- 7. 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.
- 8. LIONS, J.-L. (1969) Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod.
- 9. 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.
- 10. MORDUKHOVICH, B. S. (2006) Variational Analysis and Generalized Differentiation. II. Grundlehren der Mathematischen Wissenschaften, 331, Springer, Berlin.
- 11. 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.
- 12. RODRIGUES, J.-F. (1987) Obstacle Problems in Mathematical Physics. North-Holland Mathematics Studies, 134, North-Holland, Amsterdam.
- 13. ROUBIČEK, T. (2005) Nonlinear Partial Differential Equations with Applications. International Series of Numerical Mathematics, 153, Birkh¨auser, Basel.
- 14. SCHMIDT, S. and SCHULZ, V. (2010) Shape derivatives for general objective functions and the incompressible Navier-Stokes equations. Control Cybernet. 39, 3, 677–713.
- 15. 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.
- 16. 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.
- 17. 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.
- 18. 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.
- 19. 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.
- 20. 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
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