OPTIMAL CONTROL PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES WITH BOUNDARY CONDITIONS

다국어 초록 (Multilingual Abstract)

In this paper, we study optimal control problems for parabolic hemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control for various observation cases.

참고문헌 (Reference)

1 S. Mig´orski, "Vanishing viscosity for hemivariational inequalities modeling dynamic problems in elasticity" 66 (66): 1840-1852, 2007

2 J. P. Aubin, "Un th`eor´eme de compasit´e" 256 : 5042-5044, 1963

3 D. G. Park, "Regularity of parabolic hemivariational in-equalities with boundary conditions" 2009 : 22-, 2009

4 M. Shillor, "Recent Advances in Contact Mechanics" Pergamon Press 1998

5 F. Bonnans, "Pontryagin’s principle in the control of semilinear elliptic variational inequalities" 23 (23): 299-312, 1991

6 J. Hwang, "Parameter identification problems for an extensible beam equation" 359 (359): 682-695, 2009

7 H. Br´ezis, "Op´erateurs Maximaux Monotones et Semigroupes de Contractions dans un Espace de Hilbert" 1973

8 N. U. Ahmed, "Optimization and Identification of Systems Governed by Evolution Equa-tions on Banach Space" 1988

9 J. Hwang, "Optimal control problems for Kirchhoff type equation with a damping term" 72 (72): 1621-1631, 2010

10 V. Barbu, "Optimal control of variational inequalities, RResearch Notes in Mathematics, 100. Pitman" Advanced Publishing Program 1984

11 J. L. Lions, "Optimal Control of Systems Governed by Partial Differential Equations" Springer-Verlag 1971

12 J. Y. Park, "On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities" 55 (55): 103-113, 2003

13 J. Y. Park, "On solutions for a hyperbolic system with differential in-clusion and memory source term on the boundary" 57 (57): 459-472, 2004

14 M. Miettinen, "On parabolic hemivariational inequalities and applications" 35 (35): 885-915, 1999

15 V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Space" Nordhoff Leiden 1976

16 J. L. Lions, "Non-Homogeneous Boundary Value Problems and Appli-cations. I, II" Springer-Verlag 1971

17 P. D. Panagiotopoulos, "Modelling of nonconvex nonsmooth energy problems. Dynamic hemivariational inequalities with impact effects" 63 (63): 123-138, 1995

18 R. Dautray, "Mathematical analysis and numerical methods for science and technology" Springer-Verlag 5 : 1992

19 P. D. Panagiotopoulos, "Inequality Problems in Mechanics and Applicatons, Convex and Nonconvex Energy Functions" Birkh¨auser 1985

20 J. Rauch, "Discontinuous semilinear differential equations and multiple valued maps" 64 (64): 277-282, 1977

21 V. Barbu, "Analysis and Control of Nonlinear Infinite Dimensional Systems" Academic Press Limited 1993

22 I. Karatzas, "An Introduction to Variational Inequalities and Their Applications" Academic Press 1980

23 M. Miettinen, "A parabolic hemivariational inequality" 26 (26): 725-734, 1996