Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 27, pp. 1-19.

Title: Existence and stability of solutions for
       nonlinear Mecking-Lucke-Grilhe equations

Authors: Ali Alriyabi (Univ. de Poitiers, Cedex, France)
         Said Hilout  (Univ. de Poitiers, Cedex, France)

Abstract:
 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.

Submitted July 18, 2010 Published February 15, 2011.
Math Subject Classifications: 34A34, 34D05, 34D20, 34A45.
Key Words: Mecking-Lucke-Grilhe equation; plastic deformation;
           delay differential equations; characteristic equation;
           dislocation; asymptotic stability.