대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제54권2호
  • /
  • Pages.647-654
  • /
  • 2017
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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MODIFIED DUALITY SCHEME FOR SOLVING MODEL CRACK PROBLEM IN MECHANICS

  • Namm, Robert V. (Computing Center of Far Eastern Branch Russian Academy of Sciences) ;
  • Woo, Gyungsoo (Department of Mathematics Changwon National University)
  • 투고 : 2016.03.22
  • 발행 : 2017.03.31
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초록

Duality methods based on modified Lagrangian functional for solving a model crack problem is considered. Without additional assumptions of regularity of the solution of an initial problem duality ratio is established for initial and dual problem.

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과제정보

연구 과제 주관 기관 : Changwon National University

참고문헌

  1. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.
  2. S. Fucik and A. Kufner, Nonlinear Differential Equations, Mir, Moscow, 1988.
  3. A. M. Khludnev, Elasticity problems in non-smooth domains, Fizmatlit, Moscow, 2010.
  4. N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988.
  5. W. Maclean, Strongly Elliptic Systems and Boundary Integrals Equations, University Press, Cambridge, 2000.
  6. R. V. Namm and E. M. Vikhtenko, Modified Lagrangian functional for solving the Sig-norini problem with friction, Advances in Mechanics Research, Nova Science Publishers, New-York 1 (2011), 435-446.
  7. R. V. Namm, and G. Woo, Lagrange multiplier method for solving variational inequality in mechanics, J. Korean Math. Soc. 52 (2015), no. 6, 1195-1207. https://doi.org/10.4134/JKMS.2015.52.6.1195
  8. E. M. Vikhtenko, G. Woo, and R. V. Namm, Sensitivity Functionals in Contact Problems of Elasticity Theory, Comput. Math. Math. Phys. 54 (2014), no. 7, 1190-1200. https://doi.org/10.1134/S0965542514070112