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Minimizing movement approach using general level set functions for evolving spirals by crystalline curvature flow

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we consider evolving spirals by crystalline eikonal-curvature flow in the plane. Our focus on this issue is to propose a framework to treat the evolution of several spirals with singular diffusion by L^1 type regularization, and merging with each other. For this purpose, we consider this motion with the minimizing movement approach based on the algorithm proposed by Chambolle in 2004. This approach considers the motion of interfaces as the minimizing movement of the singular surface energy and distance from the original interface. Note that the distance is measured by the signed distance function of the interface. However, the signed distance is not well-defined since a spiral curve does not divide the domain into inside and outside of the curve. To overcome this issue, we introduce two approaches; construct a signed distance function only around the curve, or using general level set function for spirals instead of the signed distance. We present several numerical results, which is established with the split Bregman iteration. This is a joint work with Y.-H. R. Tsai.

Mathematics; Partial differential equations; Numerical analysis

video/mp4

Author affiliation: Gunma University Japan

2019-03-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68745

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/