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Browder-Tikhonov regularization for a class of evolution second order hemivariational inequalities

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Abstract

In this paper, we consider a class of evolution second order hemivariational inequalities with non-coercive operators which are assumed to be known approximately. Using the so-called Browder-Tikhonov regularization method, we prove that the regularized evolution hemivariational inequality problem is solvable. We construct a sequence based on the solvability of the regularized evolution hemivariational inequality problem and show that every weak cluster of this sequence is a solution for the evolution second order hemivariational inequality.

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References

  1. Berkovits J., Mustonen V.: Monotonicity methods for nonlinear evolution equations. Nonlinear Anal. TMA 27, 1397–1405 (1996)

    Article  Google Scholar 

  2. Carl S., Heikkilä S.: Nonlinear Differential Equations in Ordered Spaces. Chapman & Hall/CRC, Boca Raton, FL (2000)

    Google Scholar 

  3. Carl S., Motreanu D.: Extremal solutions of quasilinear parabolic inclusions with generalized Clarke’s gradient. J. Differ. Equ. 191, 206–233 (2003)

    Article  Google Scholar 

  4. Carl S., Naniewicz Z.: Vector quasi-hemivariational inequalities and discontinuous elliptic systems. J. Global Optim. 34, 609–634 (2006)

    Article  Google Scholar 

  5. Carl S., Le V.K., Motreanu D.: Existence and comparison results for quasilinear evolution hemivariational inequalities. Electron. J. Differ. Equ. 57, 1–17 (2004)

    Google Scholar 

  6. Carl S., Le V.K., Motreanu D.: The sub-supersolutio method and extremal solutions for quasilinear hemivariational inequalities. Differ. Integral Equ. 17, 165–178 (2004)

    Google Scholar 

  7. Carl S., Le V.K., Motreanu D.: Nonsmooth Variational Problems and their Inequalities, Comparison Principles and Applications. Springer-Verlag, Berlin (2005)

    Google Scholar 

  8. Clarke F.H.: Optimization and Nonsmooth Analysis. SIAM, Philadelphia (1990)

    Google Scholar 

  9. Denkowski Z., Migorski S.: Existence of solutions to evolution second order hemivariational inequalities with multivalued damping. Syst. Model. Optim. 166, 203–215 (2005)

    Article  Google Scholar 

  10. Denkowski Z., Migorski S., Papageorgiou N.S.: An Introduction to Nonlinear Analysis: Applications. Kluwer Academic Publishers, Boston, Dordrecht, London (2003)

    Google Scholar 

  11. Giannessi F., Khan A.A.: Regularization of non-coercive quasi variational inequalities. Control Cybern. 29, 91–110 (2000)

    Google Scholar 

  12. Liu Z.H.: Some convergence results for evolution hemivariational inequalities. J. Global Optim. 29, 85–95 (2004)

    Article  Google Scholar 

  13. Liu Z.H.: Browder-Tikhonov regularization on non-coercive evolution hemivariational inequalities. Inverse Probl. 21, 13–20 (2005)

    Article  Google Scholar 

  14. Migorski S.: Boundary hemivariational inequalities of hyperbolic type and applications. J. Global Optim. 31, 505–533 (2005)

    Article  Google Scholar 

  15. Motreanu D., Panagiotopoulos P.D.: Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities and Applications, Nonconvex Optimization and Its Applications, vol. 29. Kluwer Academic, Dordrecht (1999)

    Google Scholar 

  16. Naniewicz Z., Panagiotopoulos P.D.: Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, New York (1995)

    Google Scholar 

  17. Ochal A.: Existence results for evolution hemivariational inequalities of second order. Nonlinear Anal. TMA 60, 1369–1391 (2005)

    Article  Google Scholar 

  18. Panagiotopoulos P.D.: Coercive and semicoercive hemivariational inequalities. Nonlinear Anal. TMA 16, 209–231 (1991)

    Article  Google Scholar 

  19. Panagiotopoulos P.D.: Hemivariational Inequalities, Applications in Mechanics and Engineering. Springer-Verlag, Berlin (1993)

    Google Scholar 

  20. Panagiotopoulos P.D.: Hemivariational inequalitiy and fan-variational inequality. New applications and results. Atti. Sem. Mat. Fis. Univ. Modena XLIII, 159–191 (1995)

    Google Scholar 

  21. Xiao Y.B., Huang N.J.: Sub-supersolution method and extremal solutions for higher order quasi-linear elliptic hemi-variational inequalities. Nonlinear Anal. TMA 66, 1739–1752 (2007)

    Article  Google Scholar 

  22. Xiao Y.B., Huang N.J.: Generalized quasi-variational-like hemivariational inequalities. Nonlinear Anal. TMA 69, 637–646 (2008)

    Article  Google Scholar 

  23. Zeidler E.: Nonlinear Functional Analysis and its Applications, vol. II. Springer-verlag, Berlin (1990)

    Google Scholar 

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Authors and Affiliations

  1. School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, People’s Republic of China

    Yi-bin Xiao

  2. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People’s Republic of China

    Yi-bin Xiao & Nan-jing Huang

Authors
  1. Yi-bin Xiao
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  2. Nan-jing Huang
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Correspondence to Nan-jing Huang.

Additional information

This work was supported by the National Natural Science Foundation of China (10671135) and Specialized Research Fund for the Doctoral Program of Higher Education (20060610005).

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Xiao, Yb., Huang, Nj. Browder-Tikhonov regularization for a class of evolution second order hemivariational inequalities. J Glob Optim 45, 371–388 (2009). https://doi.org/10.1007/s10898-008-9380-0

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  • DOI: https://doi.org/10.1007/s10898-008-9380-0

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