Geodesic
Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations
Electronic Journal of Differential Equations, Tome 2011 (2011).

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Summary: In this article, we present the nonlinear Mecking-Lucke-Grilhe model describing the temporal evolution for simple and multi-instabilities of plastic deformation of stressed monocristal. This model extends the linear problem considered in [9, 13, 14]. Using a nonlinear analysis, we present some results of existence and stability of the solution with respect to the characteristics of the material and the retarded times. Numerical examples validating the theoretical results are also investigated in this study.
Classification : 34A34, 34D05, 34D20, 34A45
Keywords: mecking-lucke-grilhe equation, plastic deformation, delay differential equations, characteristic equation, dislocation, asymptotic stability 
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     author = {Alriyabi, Ali and Hilout, Said},
     title = {Existence and stability of solutions for nonlinear {Mecking-Lucke-Grilhe} equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a36/}
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Alriyabi, Ali; Hilout, Said. Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a36/