Source term model for elasticity system with nonlinear dissipative term in a thin domain

• Autorzy: Dilmi Mohamed , Dilmi Mourad , Boulaaras Salah , Benseridi Hamid

Identyfikatory

DOI

10.1515/dema-2022-0033

• Języki publikacji: EN

Abstrakty

EN

This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u∗ is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.

Słowa kluczowe

EN

asymptotic behavior; dissipative term; source term; Tresca friction law; weak solution

PL

zachowanie asymptotyczne; słabe rozwiązanie; równanie falowe; równania różniczkowe liniowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 437--451
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Dilmi Mohamed

• Department of Mathematics, Faculty of Science, University of Saad Dahlab-Blida 1, Blida, Algeria

autor

Dilmi Mourad

• Department of Mathematics, Applied Mathematics Laboratory, Faculty of Sciences, University of Ferhat ABBAS- Sétif 1, Sétif, 19000, Algeria

autor

Boulaaras Salah

• Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Saudi Arabia

autor

Benseridi Hamid

• Department of Mathematics, Applied Mathematics Laboratory, Faculty of Sciences, University of Ferhat ABBAS- Sétif 1, Sétif, 19000, Algeria

Bibliografia

• [1] A. Saadallah, H. Benseridi, M. Dilmi, and S. Drabla, Estimates for the asymptotic convergence of a nonisothermal linear elasticity with friction, Georgian Math. J. 23 (2016), no. 3, 435–446.
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• [3] S. Manaa, H. Benseridi, and M. Dilmi, 3D-2D asymptotic analysis of an interface problem with a dissipative term in a dynamic regime, Bol. Soc. Mat. Mex. 27 (2021), 10.
• [4] J. C. Paumier, Le problème de Signorini dans la Théorie des plaques minces de Kirchhoff-Love, C. R. Acad. Sci. Paris, Ser. I 335 (2002), 567–570.
• [5] G. Bayada and M. Boukrouche, On a free boundary problem for Reynolds equation derived from the Stokes system with Tresca boundary conditions, J. Math. Anal. Appl. 382 (2003), 212–231.
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• [7] M. A. Ragusa, Parabolic Herz spaces and their applications, Appl. Math. Lett. 25 (2012), no. 10, 1270–1273.
• [8] A. Saadallah, H. Benseridi, and M. Dilmi, Asymptotic convergence of a generalized non-Newtonian fluid with Tresca boundary conditions, Acta. Math. Sci. 40 (2016), no. 3, 700–712.
• [9] G. Duvaut and J. L. Lions, Les inéquations en mé canique des fluides, Dunod, 1969.
• [10] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.
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• [12] J. E. Lagnese, Uniform asymptotic energy estimates for solution of the equation of dynamic plane elasticity with nonlinear dissipation at the boundary, Nonlinear Anal. T. M. A. 16 (1991), 35–54.
• [13] H. A. Levine, Instability and nonexistence of global solutions to nonlinear wave equations of the form, Trans. Amer. Math. Soc. 192 (1974), 1–21.
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• [15] M. Nakao, Energy decay for the wave equation with a nonlinear weak dissipation, Differ. Integral Equ. 8 (1995), no. 3, 681–688.
• [16] M. Dilmi, M. Dilmi, and H. Benseridi, Asymptotic behavior for the elasticity system with a nonlinear dissipative term, Rend. Istit. Mat. Univ. Trieste 51 (2019), 41–60.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).