Abstract and Applied Analysis
Volume 2013 (2013), Article ID 724190, 10 pages
http://dx.doi.org/10.1155/2013/724190
Research Article

Optimal Control Problems for Nonlinear Variational Evolution Inequalities

Eun-Young Ju and Jin-Mun Jeong

Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

Received 12 November 2012; Revised 4 January 2013; Accepted 6 January 2013

Academic Editor: Ryan Loxton

Copyright © 2013 Eun-Young Ju and Jin-Mun Jeong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.