Asymptotic behavior of entire solutions to reaction-diffusion equations in an infinite star graph

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 {document}t→±∞{document} and classify the entire solutions according to their behaviors, where an entire solution is meant by a classical solution defined for all {document}t∈(-∞, ∞){document} . 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.