Open Access
| Issue |
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 2957 - 2990 | |
| DOI | https://doi.org/10.1051/m2an/2025080 | |
| Published online | 07 November 2025 | |
- R.A. Adams, Sobolev Spaces. Vol. 65 of Pure Appl. Math. Academic Press, New York, NY (1975). [Google Scholar]
- O. Alvarez, P. Cardaliaguet and R. Monneau, Existence and uniqueness for dislocation dynamics with nonnegative velocity. Interfaces Free Bound. 7 (2005) 415–434. [Google Scholar]
- O. Alvarez, E. Carlini, R. Monneau and E. Rouy, Convergence of a first order scheme for a non-local eikonal equation. Appl. Numer. Math. 56 (2006) 1136–1146. [Google Scholar]
- O. Alvarez, P. Hoch, Y. Le Bouar and R. Monneau, Dislocation dynamics: short-time existence and uniqueness of the solution. Arch. Ration. Mech. Anal. 181 (2006) 449–504. [Google Scholar]
- P.M. Anderson, J.P. Hirth and J. Lothe, Theory of Dislocations, 3rd edition. Cambridge University Press, Cambridge (2017). [Google Scholar]
- G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Vol. 17 of Math. Appl. (Berl.) Springer-Verlag, Paris (1994). [Google Scholar]
- G. Barles and O. Ley, Nonlocal first-order Hamilton-Jacobi equations modelling dislocations dynamics. Commun. Part. Differ. Equ. 31 (2006) 1191–1208. [Google Scholar]
- G. Barles, P. Cardaliaguet, O. Ley and R. Monneau, Global existence results and uniqueness for dislocation equations. SIAM J. Math. Anal. 40 (2008) 44–69. [Google Scholar]
- G. Barles, P. Cardaliaguet, O. Ley and A. Monteillet, Uniqueness results for nonlocal Hamilton-Jacobi equations. J. Funct. Anal. 257 (2009) 1261–1287. [Google Scholar]
- R. Boudjerada and A. El Hajj, Global existence results for eikonal equation with BV initial data. NoDEA, Nonlinear Differ. Equ. Appl. 22 (2015) 947–978. [Google Scholar]
- R. Boudjerada, A. El Hajj and M.S. Moulay, Existence result for a one-dimensional eikonal equation. C. R. Math. Acad. Sci. Paris 353 (2015) 133–137. [Google Scholar]
- M.G. Crandall and P.-L. Lions, Two approximations of solutions of Hamilton-Jacobi equations. Math. Comput. 43 (1984) 1–19. [Google Scholar]
- A. El Hajj, Global solution for a non-local eikonal equation modelling dislocation dynamics. Nonlinear Anal. Theory Methods Appl. Ser. A Theory Methods 168 (2018) 154–175. [Google Scholar]
- A. El Hajj and R. Monneau, Global continuous solutions for diagonal hyperbolic systems with large and monotone data. J. Hyperbolic Differ. Equ. 7 (2010) 139–164. [Google Scholar]
- A. Ghorbel and R. Monneau, Well-posedness and numerical analysis of a one-dimensional non-local transport equation modelling dislocations dynamics. Math. Comput. 79 (2010) 1535–1564. [Google Scholar]
- L. Monasse and R. Monneau, Gradient entropy estimate and convergence of a semi-explicit scheme for diagonal hyperbolic systems. SIAM J. Numer. Anal. 52 (2014) 2792–2814. [Google Scholar]
- D. Rodney, Y. Le Bouar and A. Finel, Phase field methods and dislocations. Acta Materialia 51 (2003) 17–30. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.