Boundary optimal control for systems described by parabolic problem without initial conditions(in Ukrainian) |
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Author |
amtseb@gmail.com
Ivan Franko National University of Lviv
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Abstract |
We prove the existence and uniqueness of the optimal control for systems described by
mixed boundary problem for parabolic equation without initial conditions. We investigate the
case of the boundary control and the final observation. We obtain a set of correlations that
characterize the optimal controls for such problem.
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Keywords |
parabolic equation; optimal control; Fourier problem; problem without initial conditions
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DOI |
doi:10.15330/ms.44.1.89-103
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Reference |
1. Lions J.-L. Optimal control of systems described by partial differential equations. – M.: Mir, 1972. (in
Russian)
2. Boltyanskiy V.G. Mathematical methods of optimal control. – M.: Nauka, 1969. (in Russian) 3. Balakrishnan V. Semigroup theory and control theory. – Washington, 1965. 4. Butkovsky A.G. Methods for control of systems with distributed parameters. – Ì.: Nauka, 1975. – 568 p. (in Russian) 5. Zgurovsky M.Z., Melnyk V.S., Novikov A.N. Applied methods of analysis and control of nonlinear processes and fields. – K.: Naukova dumka, 2004. – 590 p. (in Russian) 6. Zuliang L. Existance and uniquiness of second order parabolic bilinear optimal control problems// Lobachevskii Journal of mathematics. – 2011. – V.32, ¹4. – P. 320–327. 7. Bushuev I.V. On a class of optimal control problems for parabolic equations// Siberean Mathematical Journal. – 1994. – V.35, ¹5. 8. Casas E., Vexler B., Zuazua E. Sparse initial data identification for parabolic pde and its finite element approximations. – Mathematical Control and Related Fields, V.5, ¹3, 2015. 9. Gong W., Hinze M., Zhou Z. A finite element method for Dirichlet boundary control problems governed by parabolic PDEs. – Hamburger Beitrage zur Angewandten Mathematik, ¹2014-21, 2014. 10. Belgacem F.B., Bernardi Ch., Fekih H., Metoui H. On the Dirichlet boundary control of the heat equation with a final observation Part I: A space-time mixed formulation and penalization // hal.archivesouvertes. fr/hal-00400226/document. 11. Gorbonos S.O., Kogut P.I. On pathological solutions to an optimal boundary control problem for linear parabolic equation// Kibernetyka i Vychsl. technyka. – 2014. – V.176. – P. 5–18. (in Russian) 12. D. Homberg, K. Krumbiegel, J. Rehberg Optimal control of a parabolic equation with dynamic boundary condition// Applied Mathematics & Optimization. – 2013. – V.67, ¹1. – P. 3–31. 13. Pukalskyi I.D. Nonlocal boundary-value problem with degeneration and optimal control problem for linear parabolic equations// Journal of Mathematical Sciences. – 2012. – V.184, ¹1. – P. 19–35. 14. Akimenko V.V., Nakonechnyi A.G., Trofimchuk O.Yu. An optimal control model for a system of degenerate parabolic integro-differential equations // Cybernetics and Systems Analysis. – 2007. – V.43, ¹6. – P. 838–847. 15. Vlasenko L.A., Samoilenko A.M. Optimal control with impulsive component for systems described by implicit parabolic operator differential equations// Ukr. Math. Jour. – 2009. – V.61, ¹8, P. 1250–1263. 16. Bokalo M. Optimal control of evolution systems without initial conditions// Visnyk of the Lviv University. Series Mechanics and Mathematics. – 2010. – V.73. – P. 85–113. (in Ukrainian) 17. Bokalo M. M. Optimal control problem for evolution systems without initial conditions// Nonlinear boundary problem. – 2010. – V.20. – P. 14–27. (in Ukrainian) 18. Bokalo M. M., Buhrii O. M., Mashiyev R. A. Unique solvability of initial-boundary-value problems for anisotropic elliptic-parabolic equations with variable exponents of nonlinearity// Journal of nonlinear evolution equations and applications. – 2014. – V.13, ¹6. – P. 67–87. 19. Bokalo M., Lorenzi A. Linear evolution first-order problems without initial conditions// Milan Journal of Mathematics. – 2009. – V.77. – P. 437–494. 20. Showalter R. E. Monotone operators in Banach space and nonlinear partial differential equations. – Amer. Math. Soc., V.49, Providence, 1997. |
Pages |
89-103
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Volume |
44
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Issue |
1
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Year |
2015
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Journal |
Matematychni Studii
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Full text of paper | |
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