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Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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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Submitter: 数学紀要登録作業用
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