Existence of traveling domain solutions for a two-dimensional moving boundary problem
Existence of traveling domain solutions for a two-dimensional moving boundary problem
复制标题
二维移动边界问题行域解的存在性
DOI：
10.1090/s0002-9947-09-04562-0
复制
发表时间：
2009
影响因子：
1.3
通讯作者：
R. Lui
中科院分区：
文献类型：
--
作者：
Y. Choi;R. Lui
本文证明了一类二维运动边界问题的行域解的存在性。具体地说，我们证明了一个以恒定速度k向右移动的区域的存在性和一个函数b的存在性，该函数b在具有恒定Dirichlet边界条件的区域内求解多孔介质型方程。用舍费尔不动点定理来证明。该结果可以看作是作者和Juliet Lee（2004）证明的一维细胞运动模型的行细胞解存在性的延伸。
In this paper we prove the existence of a traveling domain solution for a two-dimensional moving boundary problem. Specifically, we prove the existence of a domain that travels to the right at a constant speed k and a function b which solves a porous medium type equation in the domain with constant Dirichlet boundary condition. The proof is by Schaefer's fixed point theorem. The result may be viewed as an extension of the existence of traveling cell solutions of a one-dimensional cell motility model proved by the authors and Juliet Lee (2004).