American Institute of Mathematical Sciences

Advanced
April  1999, 5(2): 279-290. doi: 10.3934/dcds.1999.5.279

Optimal control of systems governed by some elliptic equations

Urszula Ledzewicz 1, and  Stanislaw Walczak 2,

1. 

Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, United States
2. 

Department of Mathematics, University of Lodz, 90-238 Lodz, Poland

Received  June 1998 Revised  June 1998 Published  January 1999

Based on variational methods sufficient conditions for the continuous dependence of the solution of a system governed by some elliptic equation on controls is discussed. Then these conditions are used to obtain an existence theorem for the optimal control problem of a system governed by nonlinear elliptic equations with controls.
Keywords: nonlinear elliptic equations, multivalued maps., boundary value problems, Optimal control.
Mathematics Subject Classification: Primary: 49J20, 35J50; Secondary: 49K27, 35J5.
Citation: Urszula Ledzewicz, Stanislaw Walczak. Optimal control of systems governed by some elliptic equations. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 279-290. doi: 10.3934/dcds.1999.5.279
[1]

Shu Luan. On the existence of optimal control for semilinear elliptic equations with nonlinear neumann boundary conditions. Mathematical Control and Related Fields, 2017, 7 (3) : 493-506. doi: 10.3934/mcrf.2017018
[2]

Sofia Giuffrè, Giovanna Idone. On linear and nonlinear elliptic boundary value problems in the plane with discontinuous coefficients. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1347-1363. doi: 10.3934/dcds.2011.31.1347
[3]

Mark I. Vishik, Sergey Zelik. Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Communications on Pure and Applied Analysis, 2014, 13 (5) : 2059-2093. doi: 10.3934/cpaa.2014.13.2059
[4]

Olexiy V. Kapustyan, Pavlo O. Kasyanov, José Valero, Mikhail Z. Zgurovsky. Attractors of multivalued semi-flows generated by solutions of optimal control problems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1229-1242. doi: 10.3934/dcdsb.2019013
[5]

Hongbo Guan, Yong Yang, Huiqing Zhu. A nonuniform anisotropic FEM for elliptic boundary layer optimal control problems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1711-1722. doi: 10.3934/dcdsb.2020179
[6]

Xuemei Zhang, Meiqiang Feng. Double bifurcation diagrams and four positive solutions of nonlinear boundary value problems via time maps. Communications on Pure and Applied Analysis, 2018, 17 (5) : 2149-2171. doi: 10.3934/cpaa.2018103
[7]

Olha P. Kupenko, Rosanna Manzo. On optimal controls in coefficients for ill-posed non-Linear elliptic Dirichlet boundary value problems. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1363-1393. doi: 10.3934/dcdsb.2018155
[8]

Hugo Beirão da Veiga. Elliptic boundary value problems in spaces of continuous functions. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 43-52. doi: 10.3934/dcdss.2016.9.43
[9]

Gabriella Zecca. An optimal control problem for some nonlinear elliptic equations with unbounded coefficients. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1393-1409. doi: 10.3934/dcdsb.2019021
[10]

K. Q. Lan, G. C. Yang. Optimal constants for two point boundary value problems. Conference Publications, 2007, 2007 (Special) : 624-633. doi: 10.3934/proc.2007.2007.624
[11]

Leszek Gasiński, Nikolaos S. Papageorgiou. Relaxation of optimal control problems driven by nonlinear evolution equations. Evolution Equations and Control Theory, 2020, 9 (4) : 1027-1040. doi: 10.3934/eect.2020050
[12]

Felix Sadyrbaev. Nonlinear boundary value problems of the calculus of variations. Conference Publications, 2003, 2003 (Special) : 760-770. doi: 10.3934/proc.2003.2003.760
[13]

Feliz Minhós, Rui Carapinha. On higher order nonlinear impulsive boundary value problems. Conference Publications, 2015, 2015 (special) : 851-860. doi: 10.3934/proc.2015.0851
[14]

John V. Baxley, Philip T. Carroll. Nonlinear boundary value problems with multiple positive solutions. Conference Publications, 2003, 2003 (Special) : 83-90. doi: 10.3934/proc.2003.2003.83
[15]

Ming Yan, Lili Chang, Ningning Yan. Finite element method for constrained optimal control problems governed by nonlinear elliptic PDEs. Mathematical Control and Related Fields, 2012, 2 (2) : 183-194. doi: 10.3934/mcrf.2012.2.183
[16]

Santiago Cano-Casanova. Coercivity of elliptic mixed boundary value problems in annulus of $\mathbb{R}^N$. Discrete and Continuous Dynamical Systems, 2012, 32 (11) : 3819-3839. doi: 10.3934/dcds.2012.32.3819
[17]

Matthias Eller, Daniel Toundykov. Carleman estimates for elliptic boundary value problems with applications to the stablization of hyperbolic systems. Evolution Equations and Control Theory, 2012, 1 (2) : 271-296. doi: 10.3934/eect.2012.1.271
[18]

Shujie Li, Zhitao Zhang. Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 489-493. doi: 10.3934/dcds.1999.5.489
[19]

Zongming Guo, Yunting Yu. Boundary value problems for a semilinear elliptic equation with singular nonlinearity. Communications on Pure and Applied Analysis, 2016, 15 (2) : 399-412. doi: 10.3934/cpaa.2016.15.399
[20]

Piermarco Cannarsa, Carlo Sinestrari. On a class of nonlinear time optimal control problems. Discrete and Continuous Dynamical Systems, 1995, 1 (2) : 285-300. doi: 10.3934/dcds.1995.1.285

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (68)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy