A geometrical approach to front propagation problems in bounded domains with Neumann-type boundary conditions
A geometrical approach to front propagation problems in bounded domains with Neumann-type boundary conditions
复制标题
具有诺伊曼型边界条件的有界域中前传播问题的几何方法
DOI：
10.4171/ifb/79
复制
发表时间：
2003
影响因子：
1
通讯作者：
F. Lio
中科院分区：
文献类型：
--
作者：
G. Barles;F. Lio
我们感兴趣的是有界域中缩放反应扩散方程解的渐近行为，与诺伊曼型边界条件相关，更确切地说，在用移动界面描述这种行为的情况下。一个典型的例子是与斜导数边界条件相关的 Allen-Cahn 方程的情况，其中显示了在角度边界条件下按平均曲率移动的锋面的生成。为了严格地建立这样的结果，我们修改和适应了P. E. Souganidis和第一作者为解决RN问题而引入的“几何方法”：我们为具有曲率相关速度和角度边界条件的锋面全局时间运动弱解提供了新的定义，结果证明这与不存在肥化现象时的水平集方法等效。我们使用这个定义来获得一大类反应扩散方程解的渐近行为，包括拟线性方程和 (x, t) 相关反应项的情况，但也包括任何可能非线性的诺依曼边界条件。
We are interested in the asymptotic behavior of the solutions of scaled reaction-diffusion equations in bounded domains, associated with Neumann type boundary conditions, and more precisely in cases when such behavior is described in terms of moving interfaces. A typical example is the case of the Allen–Cahn equation associated with an oblique derivative boundary condition, where the generation of a front moving by mean curvature with an angle boundary condition is shown. In order to establish such results rigourously, we modify and adapt the “geometrical approach” introduced by P. E. Souganidis and the first author for solving problems in RN : we provide a new definition of weak solution for the global-in-time motion of fronts with curvature-dependent velocities and with angle boundary conditions, which turns out to be equivalent to the level-set approach when there is no fattening phenomenon. We use this definition to obtain the asymptotic behavior of the solutions of a large class of reaction-diffusion equations, including the case of quasilinear ones and (x, t)dependent reaction terms, but also with any, possibly nonlinear, Neumann boundary conditions.
影响因子：
1.4
作者：
H. Ishii;Moto-Hiko Sato
通讯作者：
H. Ishii;Moto-Hiko Sato
非光滑域上奇异简并抛物线方程的诺伊曼问题。
DOI：
--
发表时间：
2003
期刊：
京都大学数理解析研究所講究録 No. 1323
影响因子：
--
作者：
M.Kurokiba;T.Ogawa;M.-H.Sato
通讯作者：
M.-H.Sato
广义平均曲率流
DOI：
--
发表时间：
2021
期刊：
影响因子：
--
作者：
M. Sakano;M. Hirayama;T. Takahashi;S. Akebi;M. Nakayama;K. Kuroda;K. Taguchi;T. Yoshikawa;K. Miyamoto;T. Okuda;K. Ono;H. Kumigashira;T. Ideue;Y. Iwasa;N. Mitsuishi;K. Ishizaka;S. Shin;T. Miyake;S. Murakami;T. Sasagawa;and Takeshi Kondo;Yoshihiro Tonegawa
通讯作者：
Yoshihiro Tonegawa