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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 13
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Articles

Convergence of Rothe scheme for a class of dynamic variational inequalities involving Clarke subdifferential

Pages 2189-2209 | Received 26 Feb 2017, Accepted 15 Jul 2017, Published online: 02 Aug 2017

References

  • Baiocchi C , Capelo A . Variational and quasivariational inequalities: applications to free-boundary problems. Chichester: John Wiley; 1984.
  • Hlaváček I , Haslinger J , Necǎs J , et al . Solution of variational inequalities in mechanics. New York (NY): Springer-Verlag; 1988.
  • Kinderlehrer D , Stampacchia G . An introduction to variational inequalities and their applications. Vol. 31, Classics in applied mathematics. Philadelphia: SIAM; 2000.
  • Eck C , Jarušek J , Krbeč M . Unilateral contact problems: variational methods and existence theorems. Vol. 270, Pure and applied mathematics. New York (NY): Chapman/CRC Press; 2005.
  • Eck C , Jarušek J , Sofonea M . A dynamic elastic-visco-plastic unilateral contact problem with normal damped response and Coulomb friction Eur J Appl Math. 2010;21:229–251.
  • Sofonea M , Renon N , Shillor M . Stress formulation for frictionless contact of an elastic-perfectly-plastic body. Appl Anal. 2004;83:1157–1170.
  • Cocou M . Existence of solutions of a dynamic Signorini’s problem with nonlocal friction in viscoelasticity. Z Angew Math Phys. 2002;53:1099–1109.
  • Nečas J , Jarušek J , Haslinger J . On the solution of the variational inequality to the Signorini problem with small friction. Boll Unione Mat Ital. 1980;5(17B):796–811.
  • Barboteu M , Bartosz K , Han W , et al . Numerical analysis of a hyperbolic hemivariational inequality arising in dynamic contact. SIAM J Numer Anal. 2015;53:527–550.
  • Barboteu M , Bartosz K , Kalita P . An analytical and numerical approach to a bilateral contact problem with nonmonotone friction. Int J Appl Math Comput Sci. 2013;23:263–276.
  • Barboteu M , Bartosz K , Kalita P , Ramadan A . Analysis of a contact problem with normal compliance, finite penetration and nonmonotone slip dependent friction. Commun Contemp Math. 2014;16: DOI:10.1142/S0219199713500168
  • Bartosz K , Danan D , Szafraniec P . Numerical analysis of a dynamic bilateral thermoviscoelastic contact problem with nonmonotone friction law. Comput Math Appl. 2017. DOI:10.1016/j.camwa.2016.12.026
  • Clarke FH . Optimization and nonsmooth analysis. New York (NY): Wiley Interscience; 1983.
  • Naniewicz Z , Panagiotopoulos PD . Mathematical theory of hemivariational inequalities and applications. New York (NY): Marcel Dekker; 1995.
  • Panagiotopoulos PD . Nonconvex problems of semipermeable media and related topics. Z Angew Math Mech. 1985;65:29–36.
  • Panagiotopoulos PD . Hemivariational inequalities, applications in mechanics and engineering. Berlin: Springer-Verlag; 1993.
  • Migórski S , Ochal A , Sofonea M . Nonlinear inclusions and hemivariational inequalities. Models and analysis of contact problems. Vol. 26, Advances in mechanics and mathematics. New York (NY): Springer; 2013.
  • Barboteu M , Bartosz K , Han W . Numerical analysis of an evolutionary variational-hemivariational inequality with application in contact mechanics. Comput Meth Appl Mech Eng. 2017;881–897. DOI:10.1016/j.cma.2017.02.003
  • Bartosz K , Cheng X , Kalita P , et al . Rothe method for evolution variational-hemivariational inequalities. J Math Anal Appl. 2015;423:841–862.
  • Bartosz K , Sofonea M . The Rothe method for variational-hemivariational inequalities with applications to contact mechanics. SIAM J Math Anal. 2016;48:861–883.
  • Han W , Migórski S , Sofonea M . A class of variational-hemivariational inequalities with applications to frictional contact problems. SIAM J Math Anal. 2014;46:3891–3912.
  • Migórski S , Ochal A , Sofonea M . A class of variational-hemivariational inequalities in reflexive Banach spaces. J Elast. 2017;151–178. DOI:10.1007/s10659-016-9600-7.
  • Sofonea M , Han W , Migorski S . Numerical analysis of history-dependent variational-hemivariational inequalities with applications to contact problems. Eur J Appl Math. 2015;26:427–452.
  • Han J , Migórski S . Analysis of a dynamic viscoelastic unilateral contact problem with normal damped response. Nonlinear Anal : Real World Appl. 2016;28:229–250.
  • Kalita P . Convergence of Rothe scheme for hemivariational inequalities of parabolic type. Int J Numer Anal Mod. 2013;10:445–465.
  • Kalita P . Semidiscrete variable time-step θ-scheme for nonmonotone evolution inclusion. arXiv:1402.3721.
  • Han W , Migórski S , Sofonea M . Advances in variational and hemivariational inequalities. Theory, numerical analysis and applications. Vol. 33. Advances in mechanics and mathematics. New York (NY): Springer; 2015.
  • Bartosz K , Sofonea M . Modeling and analysis of a contact problem for a viscoelastic rod. Z Angew Meth Phys. 2016;67127.
  • Peng Z , Liu Z . Evolution hemivariational inequality problems with doubly nonlinearoperators. J Global Opt. 2011;51:413–427.
  • Peng Z , Liu Z , Liu X . Boundary hemivariational inequality problems with doublynonlinear operators. Math Ann. 2013;356:1339–1358.
  • Denkowski Z , Migórski S , Papageorgiou NS . An introduction to nonlinear analysis: applications. Boston: Kluwer Academic/Plenum Publishers; 2003.
  • Le VK . Range and existence theorem for pseudomonotone perturbations of maximal monotone operators. Proc Amer Math Soc. 2011;139:1645–1658.
  • Roubiček T . Nonlinear partial differential equations with applications. Basel: Birkhäuser Verlag; 2005.
  • Nagase H . On an application of Rothe method to nonlinear parabolic variational inequalities. Funkc Ekvacioj. 1989;32:273–299.
  • Han W , Sofonea M . Quasistatic contact problems in viscoelasticity and viscoplasticity. Vol. 30, Studies in advanced mathematics. Providence (RI): Americal Mathematical Society, Somerville (MA): RI-International Press; 2002.
  • Denkowski Z , Migórski S , Papageorgiou NS . An introduction to nonlinear analysis: theory. Boston: Kluwer Academic/Plenum Publishers; 2003.
  • Migórski S , Ochal A . Quasi-static hemivariational inequality via vanishing acceleration approach. SIAM J Math Anal. 2009;41:1415–1435.

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