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**Boundary hemivariational inequalities of hyperbolic type and applications.**
*(English)*
Zbl 1089.49014

The author establishes two important existence results for dynamic hemivariational inequalities of hyperbolic type with multidimensional potential laws. The basic tool in the proofs is a surjectivity result involving pseudomonotone operators. The method of proof consists in transforming the problems in evolution inclusions of first order with regular data and then by using a priori estimates to pass to the limit for achieving the conclusions. The author improves previous results by assuming less restrictive hypotheses on the locally Lipschitz functions generating the subdifferential relations. Applications to dynamic viscoelastic contact problems are also presented.

Reviewer: Dumitru Motreanu (Perpignan)

### MSC:

49J40 | Variational inequalities |

47J20 | Variational and other types of inequalities involving nonlinear operators (general) |

74H20 | Existence of solutions of dynamical problems in solid mechanics |

35L85 | Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators |

74M15 | Contact in solid mechanics |

### Keywords:

hyperbolic hemivariational inequalities; multifunction; subdifferential; pseudomonotone operator; viscoelasticity
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\textit{S. Migorski}, J. Glob. Optim. 31, No. 3, 505--533 (2005; Zbl 1089.49014)

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### References:

[7] | Chau, O., Shillor, M. and Sofonea, M. (2001), Dynamic frictional contact with adhesion, J. Appl. Math. Physics, to appear · Zbl 1064.74132 |

[10] | Gasin ski, L., (2000), Hyperbolic Hemivariational Inequalities and their Applications to Optimal Shape Design, PhD Thesis, Jagiellonian Univ., Cracow, Poland, in Polish, p. 61 |

[13] | Goele ven, D. and Motreanu, D. (2001), Hyperbolic hemivariational inequality and nonlinear wave equation with discontinuities. In: Gilbert, R.P. et al. (eds.), From Convexity to Nonconvexity, Kluwer, pp. 111–122 · Zbl 1043.49010 |

[20] | Migo rski, S. (1998), Identification of nonlinear heat transfer laws in problems modeled by hemivariational inequalities, In: Tanaka, M. and Dulikravich, G.S. (eds), Proceedings of International Symposium on Inverse Problems in Engineering Mechanics 1998 (ISIP’98), Elsevier Science B.V., pp. 27–37 |

[24] | Migo rski, S., (2003), Modeling, analysis and optimal control of systems governed by hemivariational inequalities, In: Misra, J.C. (ed.), Industrial Mathematics and Statistics dedicated to commemorate the Golden Jubilee of Indian Institute of Technology, Kharagpur, India, 2002, invited paper, Narosa Publishing House |

[26] | Migo rski S., and Ochal A., (2002), Existence of solutions to boundary parabolic hemivariational inequalities, In: Baniatopoulos, C.C. (ed.), Proceeding of the International Conference on Nonsmooth Nonconvex Mechanics with Applications in Engineering, Thessaloniki, Greece, July 5-6, 2002, Ziti Editions, pp. 53–60 |

[33] | Panag iotopoulos, P.D. (1995), Hemivariational inequalities and Fan-variational inequalities. New applications and results, Atti Sem. Mat. Fis. Univ. Modena, XLIII, 159–191 |

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