Mathematics – Analysis of PDEs
Scientific paper
2009-03-08
Mathematics
Analysis of PDEs
Scientific paper
We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied stress. The equations are written on a bounded interval with Dirichlet boundary conditions and require special attention to the boundary. We prove a result of global existence of a solution. The method of the proof consists in considering first a parabolic regularization of the full system, and then passing to the limit. We show some uniform bounds on this solution which uses in particular an entropy estimate for the densities.
Ibrahim Hassan
Jazar Mustapha
Monneau Régis
No associations
LandOfFree
Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics of dislocation densities in a bounded channel. Part II: existence of weak solutions to a singular Hamilton-Jacobi/parabolic strongly coupled system will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-496918