1996 Fiscal Year Final Research Report Summary
Analysis for the Moving of Interfaces
| Project/Area Number |
06640264
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | Hokkaido Tokai University |
|---|
Principal Investigator |
CHEN Yun-Gang Hokkaido Tokai University, Research Institute for Higher Education Programs, Associated Professor, 教育開発研究センター, 助教授 (50217262)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
GIGA Yoshikazu Hokkaido University, Faculty of Science, Professor, 理学部, 教授 (70144110)
|
|---|
| Project Period (FY) |
1994 – 1996
|
| Keywords | motion of surface / mean curvature / level surface method / continuous solution / singlular point / diffusion equation / extinction / existence |
|---|
| Research Abstract |
(1) A class of nonlinear partial differential equations concerning the interface (closed surface) moving problem are studied. In particular, the mean curvature flow problem is studied with a general consideration. The level surface approach with the viscosity solution theory are applied to the analysis for the nonlinear equations (generalized mean curvature flow equations) with singularities where the gradient of the solution vanishes.
(2) The level surface method is valid for the moving surface model even when some singularity occurs, and the motion can be tracked through the time when singularity appears. This makes it possible to study the behavior near the singular points of a closed surface at the singular time, which denoting the cases when a surface extincts, or pinches, or divided into two or more parts.
(3) The profile of the solution, before and after the time when a singularity occurs, was studied analytically and numerically. Some asymptotic property of the solution was found for a kind of related equations, nonlinear diffusion equations with very fast diffusion term.
(4) Numerical methods, especially the finite difference method for the concerned nonlinear partial differential equations, are studied and a class of stable difference schemes are constructed.
|
