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Authors

MOHAMED DILMI University of Blida 1 Author https://orcid.org/0000-0003-2114-8891
MOURAD DILMI Setif 1 University, Author https://orcid.org/0000-0003-3767-5653

DOI:

https://doi.org/10.69717/ijams.v2.i2.143

Keywords:

Asymptotic analysis, Dynamic elasticity system, Frictional boundary conditions, Variational formulation

Abstract

In this article, we investigate the asymptotic behavior of solutions to a dynamic linear elasticity problem in a thin domain Ω  ⊂ R3, characterized by a nonlinear source term  and mixed boundary conditions: a strongly nonlinear friction law on one part of the boundary and a Dirichlet condition on the remainder. Our primary goal is to analyze the limiting behavior of the displacement field  as the thickness parameter  tends to zero.

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Author Biographies

  • MOHAMED DILMI, University of Blida 1

    LAMDA-RO Laboratory, Department of Mathematics, University of Blida 1, Po. Box 270 Soumaa, Blida, Algeria 

  • MOURAD DILMI, Setif 1 University,

    Applied Mathematics Laboratory, Department of Mathematics, Setif 1 University, 19000, Algeria

References

Dilmi, M. (2025). Asymptotic behavior of a nonlinear viscoelastic problems with Tresca friction law in a thin domain: M. Dilmi. Journal of Elliptic and Parabolic Equations, 11(1), 115-134. Google Scholar. https://doi.org/10.1007/s41808-024-00310-7.

Dilmi. M, Dilmi. M, Benseridi. H(2019)., Asymptotic behavior for the elasticity system with a nonlinear dissipative term, Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste, 51, pp. 41-60. https://doi.org/10.13137/2464-8728/27066

Dilmi, M., Dilmi, M., & Benseridi, H. (2019). Asymptotic analysis of quasistatic electro‐viscoelastic problem with Tresca's friction Law. Computational and Mathematical Methods, 1(3), e1028.‏ Google Scholar. https://doi.org/10.1002/cmm4.1028.

Chacha, D. A., & Miloudi, M. (2012). Asymptotic analysis of nonlinearly elastic shells “mixed approach”. Asymptotic Analysis, 80(3-4), 323-346.‏ Google Scholar. https://doi.org/10.3233/ASY-2012-1119

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Dilmi, M., & Otmani, S. (2023). Existence and asymptotic stability for generalized elasticity equation with variable exponent. Opuscula Mathematica, 43(3), 409-428.‏ Google Scholar. https://doi.org/10.7494/OpMath.2023.43.3.409.

Hale, J. K. (1992). Reaction-diffusion equation on thin domains. J. Math. Pures Appl., 71, 33-95.‏ Google Scholar.

Raugel, G. (1995). Dynamics of partial differential equations on thin domains in Dynamical systems (Montecatini Terme, 1994), 208-315. Lecture Notes in Math, 1609.‏ Google Scholar.

Dilmi, M., & Dilmi, M. (2025). EXISTENCE, UNIQUENESS AND ASYMPTOTIC ANALYSIS FOR A BOUNDARY VALUE PROBLEM WITH RIEMANN–LIOUVILLE FRACTIONAL DERIVATIVE. Memoirs on Differential Equations and Mathematical Physics, 95, 1-18.‏ Google Scholar.

Ciarlet, P. G. (1997). Mathematical elasticity. Theory of plates, vol. II. Studies in Mathematics and its Applications, 27.‏ Google Scholar. View.

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Published

2025-11-19

Issue

Vol. 2 No. 2 (2025): IJAMS 2992-1708

Section

Articles

License

Copyright (c) 2025 International Journal of Applied Mathematics and Simulation

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Asymptotic Analysis of a Dynamic Elasticity System withNonlinear Source Term  and Frictional Boundary Conditions in Thin Domains. (2025). International Journal of Applied Mathematics and Simulation, 2(2), 13-25. https://doi.org/10.69717/ijams.v2.i2.143