How to unify the total/local-lenght-constraints of the gradient flow for the bending energy of plane curves

Title:

How to unify the total/local-lenght-constraints of the gradient flow for the bending energy of plane curves

Creator:

Miyamoto, Yuki, Nagasawa, Takeyuki, and Suto, Fumito

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:75602115-0e95-48d5-a23e-3dbe38e69a5e
uuid:75602115-0e95-48d5-a23e-3dbe38e69a5e

Subject:

gradient flow, bending energy, total-lenght constraint, and local-length constraint

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The gradient flow of bending energy for plane curve is studied. The flow is considered under two kinds of constraints; one is under the area and total-length constraints; the other is under the area and local-length constraints. The fundamental results (the local existence and uniqueness) were obtained independently by Kurihara and the second author for the former one; by Okabe for the later one. For the former one the global existence was shown for any smooth initial curves, but the asymptotic behavior has not been studied. For the later one, the global existence was guaranteed for only curves with the rotation number one, and the behavior was well studied. It is desirable to compensate the results with each other. In this note, it is proposed how to unify the two flows.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[615]-624

Source:

Kybernetika | 2009 Volume:45 | Number:4

Harvested from:

CDK

Metadata only:

false