본문 바로가기
KERD
논문KCI 등재

OPTIMAL CONTROL PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES WITH BOUNDARY CONDITIONS

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

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.

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 (23)

  1. N. U. Ahmed, "Optimization and Identification of Systems Governed by Evolution Equa-tions on Banach Space", Longman Scientific and Techniacal (1988)
  2. J. P. Aubin, "Un th`eor´eme de compasit´e", C. R. Acad. Sci, 256, pp.5042~5044 (1963)
  3. V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Space" (1976), Nordhoff Leiden
  4. V. Barbu, "Optimal control of variational inequalities, RResearch Notes in Mathematics, 100. Pitman" (1984), Advanced Publishing Program
  5. V. Barbu, "Analysis and Control of Nonlinear Infinite Dimensional Systems" (1993), Academic Press Limited
  6. F. Bonnans, "Pontryagin’s principle in the control of semilinear elliptic variational inequalities", Appl. Math. Optim, 23(3), pp.299~312 (1991)
  7. H. Br´ezis, "Op´erateurs Maximaux Monotones et Semigroupes de Contractions dans un Espace de Hilbert" (1973)
  8. R. Dautray, "Mathematical analysis and numerical methods for science and technology", Evolution Problems, 5 (1992), Springer-Verlag
  9. J. Hwang, "Parameter identification problems for an extensible beam equation", J. Math. Anal. Appl, 359(2), pp.682~695 (2009)
  10. J. Hwang, "Optimal control problems for Kirchhoff type equation with a damping term", Nonlinear Anal, 72(3-4), pp.1621~1631 (2010)
  11. I. Karatzas, "An Introduction to Variational Inequalities and Their Applications" (1980), Academic Press
  12. J. L. Lions, "Optimal Control of Systems Governed by Partial Differential Equations" (1971), Springer-Verlag
  13. J. L. Lions, "Non-Homogeneous Boundary Value Problems and Appli-cations. I, II" (1971), Springer-Verlag
  14. M. Miettinen, "A parabolic hemivariational inequality", Nonlinear Anal, 26(4), pp.725~734 (1996)
  15. M. Miettinen, "On parabolic hemivariational inequalities and applications", Nonlinear Anal, 35(7), pp.885~915 (1999)
  16. S. Mig´orski, "Vanishing viscosity for hemivariational inequalities modeling dynamic problems in elasticity", Nonlinear Anal, 66(8), pp.1840~1852 (2007)
  17. J. Rauch, "Discontinuous semilinear differential equations and multiple valued maps", Proc. Amer. Math. Soc, 64(2), pp.277~282 (1977)
  18. M. Shillor, "Recent Advances in Contact Mechanics" (1998), Pergamon Press
  19. P. D. Panagiotopoulos, "Inequality Problems in Mechanics and Applicatons, Convex and Nonconvex Energy Functions" (1985), Birkh¨auser
  20. P. D. Panagiotopoulos, "Modelling of nonconvex nonsmooth energy problems. Dynamic hemivariational inequalities with impact effects", J. Comput. Appl. Math, 63(1-3), pp.123~138 (1995)
  21. D. G. Park, "Regularity of parabolic hemivariational in-equalities with boundary conditions", J. Inequal. & Appl, 2009, pp.22~ (2009)
  22. J. Y. Park, "On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities", Nonlinear Anal, 55(1-2), pp.103~113 (2003)
  23. J. Y. Park, "On solutions for a hyperbolic system with differential in-clusion and memory source term on the boundary", Nonlinear Anal, 57(3), pp.459~472 (2004)

관련 논문AI추천

이 간행물의 다른 논문 (11건)