A transport formulation of moving fronts and application to dislocations dynamics

نویسنده

  • R. Monneau
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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تاریخ انتشار 2007