Asymptotic behavior of entire solutions to reaction-diffusion equations in an infinite star graph
Shuichi Jimbo, Yoshihisa Morita
Abstract
<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ t\to\pm\infty $\end{document}</tex-math></inline-formula> and classify the entire solutions according to their behaviors, where an entire solution is meant by a classical solution defined for all <inline-formula><tex-math id="M2">\begin{document}$ t\in(-\infty, \infty) $\end{document}</tex-math></inline-formula>. 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.