Preprint
(2001)

Author(s):  
       S. Migórski, migorski(at)softlab.ii.uj.edu.pl
      
       Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland

Pages: 32

Abstract: The paper presents a survey on the mathematical modeling of nonconvex and nonsmooth problems arising in mechanics and engineering. The approach to such problems is based on the notion of hemivariational inequality and focuses on three aspects. First we present the ideas leading to inequality problems encountered in mechanics and we formulate different forms of hemivariational inequalities. Then we give results on the existence of solutions to hemivariational inequalities of elliptic, parabolic and hyperbolic types. Finally for these three types of hemivariational inequalities we formulate the optimal control problems and provide conditions under which they admit optimal solutions.

Keywords: Hemivariational inequalities, subdifferential, multifunction, control problem, nonconvex.

Published: Chapter 7 in the book "Industrial Mathematics and Statistics" dedicated to commemorate the Golden Jubilee of Indian Institute of Technology, Kharagpur, India, 2002, invited paper, Misra J.C., (ed.), Narosa Publishing House, New Delhi, India, (2003), 248-279.