A transport formulation of moving fronts and application to dislocations dynamics
نویسنده
چکیده
In this article, we consider hypersurfaces moving with normal velocity depending on the timespace 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. AMS Classification: 35R35, 35F20.
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