We deal with the bistable reaction-diffusion equation in an infinite star graph, which consists of several half-lines with a common end point. The aim of our study is to show the existence of front-like entire solutions together with the asymptotic behaviors as $ t\to\pm\infty $ and classify the entire solutions according to their behaviors, where an entire solution is meant by a classical solution defined for all $ t\in(-\infty, \infty) $. To this end, we give a condition under that the front propagation is blocked by the emergence of standing stationary solutions. The existence of an entire solution which propagates beyond the blocking is also shown.

中文翻译：

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无限星图中反应扩散方程整体解的渐近行为

我们在无限星图中处理双稳态反应扩散方程，该星方程由具有共同终点的几条半线组成。我们研究的目的是证明前似整体解的存在以及渐近行为$ t \ to \ pm \ infty $的存在，并根据其行为对整个解进行分类，其中整个解由经典表示为所有$ t \ in（-\ infty，\ infty）$定义的解决方案。为此，我们给出了一个条件，即前方传播被固定的固定解的出现所阻止。还显示了传播超出阻止范围的整个解决方案的存在。