Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

A CONVERGENCE RESULTS FOR ANTIPLANE CONTACT PROBLEM WITH TOTAL SLIP RATE DEPENDENT FRICTION

  • AMMAR, DERBAZI (Faculty of Mathematics and Informatics, Department of Mathematics, University Mohamed)
  • 투고 : 2020.10.06
  • 심사 : 2020.12.31
  • 발행 : 2021.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this work, we present the classical formulation for the antiplane problem of a eletro-viscoelastic materialswith total sliprate dependent friction and write the corresponding variational formulation. In the second step, we prove that the solution converges to the solution of the corresponding electro-elastic problem as the viscosity converges to zero.

키워드

과제정보

First of all, we would like to thank the referees for their constructive and detailed comments which helped to improve the manuscript. We have tried to incorporate all comments as good as possible.The authors would like to thank the reviewer for his/her comments that helped to improve the manuscript.

참고문헌

  1. A. Borrelli, C.O. Horgan and M.C. Patria, Saint-Venant's principle for antiplane shear deformations of linear piezoelectic materials, SIAM J. Appl. Math. 62 (2002), 2027-2044. https://doi.org/10.1137/S0036139901392506
  2. H. Brezis, Problemes unilateraux, J. Math. Pures Appl. 51 (1972), 1-168.
  3. M. Campillo and I.R. Ionescu, Initiation of antiplane shear instability under slip dependent friction, Journal of Geophysical Research 102 (1997), 363-371. https://doi.org/10.1029/96JA03106
  4. M. Dalah, Analysis of a Electro-Viscoelastic Antiplane Contact Problem With Total Slip-Rate Dependent Friction, Electronic. J. Differential Equations 2009 (2009), 1-16.
  5. M. Dalah and F.L. Rahmani, Study and analysis of an antiplane electro-elastic contact problem with Tresca friction law, I.J.R.R.A.S. 12 (2012), 1-14.
  6. A. Derbazi, M. Dalah and A. Megrous, The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory, Applications of Mathematics 61 (2016), 339-358. https://doi.org/10.1007/s10492-016-0135-9
  7. G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976.
  8. K. Fernane and M. Dalah, A. Ayadi, Existence and uniqueness solution of a quasistatic electro-elastic antiplane contact problem with Tresca friction law, Applied Sciences 14 (2012), 45-59.
  9. A. Matei and T.V. Hoarau-Mantel, Problemes antiplans de contact avec frottement pour des materiaux viscoelastiques a memoire longue, Annals of University of Craiova, Math. Comp. Sci. Ser. 32 (2005), 200-206.
  10. A. Matei, V.V. Motreanu and M. Sofonea, A Quasistatic Antiplane Contact Problem With Slip Dependent Friction, Advances in Nonlinear Variational Inequalities 4 (2001), 1-21.
  11. A. Megrous, A. Derbazi and M. Dalah, Existence and uniqueness of the weak solution for a contact problem, J. Nonlinear Sci. Appl. 9 (2016), 186-199. https://doi.org/10.22436/jnsa.009.01.17
  12. M. Sofonea, M. Dalah and A. Ayadi, Analysis of an antiplane electro-elastic contact problem, Adv. Math. Sci. Appl. 17 (2007), 385-400.