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Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84140

Title: Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term
Authors: Giga, Yoshikazu Browse this author
Gorka, Przemyslaw Browse this author
Rybka, Piotr Browse this author
Keywords: singular energies
bending of facets
driven curvature flow
variational principle
Hamilton-Jacobi equation
Issue Date: 28-Dec-2011
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 993
Start Page: 1
End Page: 35
Abstract: We study the motion of regular bent rectangles driven by singular curvature flow with a driving term. The curvature is being interpreted as a solution to a minimization problem. The evolution equation becomes in a local coordinate a system of Hamilton-Jacobi equations with free boundaries, coupled to a system of ODE’s with nonlocal nonlinearities. We establish local-in-time existence of variational solutions to the flow and uniqueness is proved under additional regularity assumptions on the data.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69799
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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