Entire solutions with merging three fronts to the Allen-Cahn equation

Yan-Yu Chen Tamkang University Jong-Shenq Guo Tamkang University Hirokazu Ninomiya Meiji University Chih-Hong Yao Tamkang University

Analysis of PDEs mathscidoc:1609.03007

2016.8
In this paper, we study entire solutions of the Allen-Chan equation in one-dimensional Euclidean space. This equation is a scalar reaction-diffusion equation with a bistable nonlinearity. It is well-known that this equation admits three different types of traveling fronts connecting two of its three constant states. Under certain conditions on the wave speeds, the existence of entire solutions with merging these three traveling fronts is shown by constructing a suitable pair of super-sub-solutions.
reaction-diffusion equation, traveling front, entire solution, super-sub-solutions
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@inproceedings{yan-yu2016entire,
  title={Entire solutions with merging three fronts to the Allen-Cahn equation},
  author={Yan-Yu Chen, Jong-Shenq Guo, Hirokazu Ninomiya, and Chih-Hong Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160915064809036799007},
  year={2016},
}
Yan-Yu Chen, Jong-Shenq Guo, Hirokazu Ninomiya, and Chih-Hong Yao. Entire solutions with merging three fronts to the Allen-Cahn equation. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160915064809036799007.
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