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Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Stability for evolving graphs by nonlocal weighted curvature
| Title: | Stability for evolving graphs by nonlocal weighted curvature |
| Authors: | Giga, M.-H Browse this author | | Giga, Y. Browse this author |
| Issue Date: | 1-Mar-1997 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 372 |
| Start Page: | 1 |
| End Page: | 70 |
| Abstract: | A general stability and convergence theorem is established for generalized solutions of a family of nonlinear evolution equations with nonlocal diffusion in one space dimension. As the first application motion by nonlocal weighted curvature is approximated by solutions of regular problem, when initial curve is given as the graph of a continuous periodic function. This justifies the motion by crystalline energy as a limit of regularized problems. As the second application the motion by crystalline energy is shown to approximate the motion by regular interfacial energy if the crystalline energy approximates the regular energy. This gives the convergence of crystalline algorithm for general curvature flow equations. Our general results are also important to explain that geometric evolution of crystals depends continuously on temperature even if facets appear. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69122 |
| 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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