A caricature of a singular curvature flow in the plane

Details A caricature of a singular curvature flow in the plane A caricature of a singular curvature flow in the plane

2008-03-25

arxiv.org/abs/0803.3513v1

Mathematics

Analysis of PDEs

Scientific paper

10.1088/0951-7715/21/10/005

We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak solutions to the semi-discretization of the problem as well as convergence of the approximating sequences. The semi-discretization shows that facets must form. For a class of initial data we are able to study in details the facet formation and interactions and their asymptotic behavior. We notice that our qualitative results may be interpreted with the help of a special composition of multivalued operators.

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