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Evolving graphs by singular weighted curvature
Title: | Evolving graphs by singular weighted curvature |
Authors: | Giga, M.-H Browse this author | Giga, Y. Browse this author |
Issue Date: | 1-Mar-1996 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 331 |
Start Page: | 1 |
End Page: | 94 |
Abstract: | A new notion of solutions is introduced to study degenerate nonlinear parabolic equations in one space dimension whose diffusion effect is so strong at particular slopes of unknowns that the equation is no longer a partial differential equation. Extending the theory of viscosity solutions comparison principle is established. For a periodic continuous initial data a unique global continuous solution (periodic in space) is constructed. The theory applies to motion of interfacial curves by crystalline energy or more generally by anisotropic interlacial energy with corners when the curves are the graphs of functions. Even if the driving force term exists, the initial value problem is solvable for general nonadmissible continuous (periodic) initial data. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69081 |
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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