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J. Korean Math. Soc. 2008; 45(3): 757-769

Printed May 1, 2008

Copyright © The Korean Mathematical Society.

Optimal control problems for semilinear evolution equations

Jin-Mun Jeong, Jin-Ran Kim, and Hyun-Hee Roh

Pukyong National University, Pukyong National University, Pukyong National University

Abstract

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This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

Keywords: nonlinear evolution equation, admissible control, time optimal control, cost function

MSC numbers: Primary 35B37, 93C20

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