A transport formulation of moving fronts and application to dislocation dynamics
Interfaces and free boundaries, Tome 9 (2007) no. 3, pp. 383-409
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In this article, we consider hypersurfaces moving with normal velocity depending on the time-space coordinates and on the normal to the hypersurface. We naturally define a measure associated to this hypersurface. This measure is defined on a suitable space/unit normal/curvature configuration space. We show that, while the hypersurface stays smooth, then the measure is a solution to a linear transport equation, that we call a transport formulation. In the particular case of curves moving in the plane, we get a simple transport formulation. With this transport formulation in hands, it is then easy to complete the models of dislocations densities that were proposed in the 60's. As a consequence, we therefore propose a closed mean field model for the dynamics of dislocations densities.
Classification :
35-XX, 65-XX, 76-XX, 92-XX
Affiliations des auteurs :
Régis Monneau 1
Régis Monneau. A transport formulation of moving fronts and application to dislocation dynamics. Interfaces and free boundaries, Tome 9 (2007) no. 3, pp. 383-409. doi: 10.4171/ifb/170
@article{10_4171_ifb_170,
author = {R\'egis Monneau},
title = {A transport formulation of moving fronts and application to dislocation dynamics},
journal = {Interfaces and free boundaries},
pages = {383--409},
year = {2007},
volume = {9},
number = {3},
doi = {10.4171/ifb/170},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/170/}
}
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