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Transition fronts in unbounded domains with multiple branches
Calculus of Variations and Partial Differential Equations ( IF 2.1 ) Pub Date : 2020-09-10 , DOI: 10.1007/s00526-020-01825-2
Hongjun Guo

This paper is concerned with the existence and uniqueness of transition fronts of a general reaction-diffusion-advection equation in domains with multiple branches. In this paper, every branch in the domain is not necessary to be straight and we use the notions of almost-planar fronts to generalize the standard planar fronts. Under some assumptions of existence and uniqueness of almost-planar fronts with positive propagating speeds in extended branches, we prove the existence of entire solutions emanating from some almost-planar fronts in some branches. Then, we get that these entire solutions converge to almost-planar fronts in some of the rest branches as time increases if no blocking occurs in these branches. Finally, provided by the complete propagation of every front-like solution emanating from one almost-planar front in every branch, we prove that there is only one type of transition fronts, that is, the entire solutions emanating from some almost-planar fronts in some branches and converging to almost-planar fronts in the rest branches.



中文翻译:

具有多个分支的无界域中的转换前沿

本文涉及具有多个分支的区域中的一般反应扩散对流方程的过渡前沿的存在和唯一性。在本文中,域中的每个分支都不必是直的,我们使用近似平面的前沿的概念来概括标准的平面前沿。在扩展分支中具有正传播速度的近似平面前沿的存在和唯一性的一些假设下,我们证明了某些分支中某些近似平面前沿产生的整体解的存在。然后,如果这些分支中没有发生阻塞,随着时间的增加,我们将获得全部解决方案收敛到某些其余分支中几乎平面的前沿。最后,从每个分支中几乎一个平面前端发出的每个前端样解的完全传播,

更新日期:2020-09-11
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