Optimal control of systems governed by some elliptic equations

Urszula Ledzewicz; Stanislaw Walczak

doi:10.3934/dcds.1999.5.279

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1999, Volume 5, Issue 2: 279-290. Doi: 10.3934/dcds.1999.5.279

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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
2.
Department of Mathematics, University of Lodz, 90-238 Lodz

Received: May 31, 1998

Revised: May 31, 1998

Published: March 1999

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Abstract

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.

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Mathematics Subject Classification: Primary: 49J20, 35J50; Secondary: 49K27, 35J55.

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