Hassan Ibrahim
Abstract:
In this article, we consider a coupled singular parabolic system,
describing the dynamics of dislocation densities in a bounded domain.
The model takes into consideration the short-range interactions between
dislocations, which causes the singularity that appears under the form
of dividing by a gradient term. We prove a long time existence and uniqueness
under the assumption that the applied stresses on the domain is bounded in
space and time. The proof relies on a comparison principle to avoid singularity,
and on exponential gradient estimates for the long time existence.
Submitted January 9, 2015. Published February 12, 2015.
Math Subject Classifications: 35K50, 35K40, 35K55.
Key Words: Boundary value problem; parabolic system; comparison principle.
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Hassan Ibrahim Lebanese University, Faculty of Sciences I EDST, Equipe EDP-AN Hadath-Beirut, Lebanon email: ibrahim@cermics.enpc.fr |
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