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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 & Continuous Dynamical Systems, 1999, 5 (2) : 279-290. doi: 10.3934/dcds.1999.5.279
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