Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations
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 r...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2011-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/27/abstr.html |
| _version_ | 1828950012603662336 |
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| author | Ali Alriyabi Said Hilout |
| author_facet | Ali Alriyabi Said Hilout |
| author_sort | Ali Alriyabi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T06:17:18Z |
| format | Article |
| id | doaj.art-5d2ab05bd6444efa906ce318f5960046 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T06:17:18Z |
| publishDate | 2011-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-5d2ab05bd6444efa906ce318f59600462022-12-21T23:13:59ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-02-01201127,119Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equationsAli AlriyabiSaid HiloutIn 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.http://ejde.math.txstate.edu/Volumes/2011/27/abstr.htmlMecking-Lucke-Grilhe equationplastic deformationdelay differential equationscharacteristic equationdislocationasymptotic stability |
| spellingShingle | Ali Alriyabi Said Hilout Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations Electronic Journal of Differential Equations Mecking-Lucke-Grilhe equation plastic deformation delay differential equations characteristic equation dislocation asymptotic stability |
| title | Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations |
| title_full | Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations |
| title_fullStr | Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations |
| title_full_unstemmed | Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations |
| title_short | Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations |
| title_sort | existence and stability of solutions for nonlinear mecking lucke grilhe equations |
| topic | Mecking-Lucke-Grilhe equation plastic deformation delay differential equations characteristic equation dislocation asymptotic stability |
| url | http://ejde.math.txstate.edu/Volumes/2011/27/abstr.html |
| work_keys_str_mv | AT alialriyabi existenceandstabilityofsolutionsfornonlinearmeckingluckegrilheequations AT saidhilout existenceandstabilityofsolutionsfornonlinearmeckingluckegrilheequations |