Optimal control problems for quasi-variational inequalities and its numerical approximation

Pages: 1101 - 1110, Issue Special, September 2011

 Abstract        Full Text (312.2K)              

Yusuke Murase - Department of Mathematics, Faculty of Science and Technology, Meijo University, 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya, 468-8502, Japan (email)
Atsushi Kadoya - Faculty of Economic Sciences, Hiroshima Shudo University, 1-1-1 Ozukahigashi, Asaminami-ku, Hiroshima, 731-3195, Japan (email)
Nobuyuki Kenmochi - Department of Education, School of Education, Bukkyo University, 96 Kitahananobo-cho, Murasakino, Kita-ku, Kyoto, 603-8301, Japan (email)

Abstract: The main objective of this paper is to discuss about optimal control problems in which the state equations may have multiple solutions. Our state equations are represented by the so-called quasi-variational inequalities and some difficulties for the mathematical treatment arise from such a structure. From the numerical point of view we propose a class of regular approximations for them in which state equations are uniquely solved and the control spaces are relaxed, and further a class of their time-discretizations which are schemes of usual elliptic optimal control problems.

Keywords:  Quasi-variational Inequality, Environmental Constraint, Reaction- Diff usion
Mathematics Subject Classification:  Primary: 35K45; Secondary: 35K50

Received: August 2010;      Revised: April 2011;      Published: October 2011.