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• W2007190407 abstract "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." @default.
• W2007190407 created "2016-06-24" @default.
• W2007190407 creator A5071780978 @default.
• W2007190407 date "2007-01-01" @default.
• W2007190407 modified "2023-09-29" @default.
• W2007190407 title "A transport formulation of moving fronts and application to dislocation dynamics" @default.
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• W2007190407 doi "https://doi.org/10.4171/ifb/170" @default.
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