Asymptotic behavior of entire solutions to reaction-diffusion equations in an infinite star graph
Asymptotic behavior of entire solutions to reaction-diffusion equations in an infinite star graph
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DOI：
10.3934/dcds.2021026
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发表时间：
2021
影响因子：
1.1
通讯作者：
S. Jimbo;Y. Morita
中科院分区：
文献类型：
--
作者：
S. Jimbo;Y. Morita
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 \begin{document}$ t\to\pm\infty $\end{document} and classify the entire solutions according to their behaviors, where an entire solution is meant by a classical solution defined for all \begin{document}$ t\in(-\infty, \infty) $\end{document} . To this end, we give a condition under that the front propagation is blocked by the emergence of standing stationary solutions. The existence of an entire solution which propagates beyond the blocking is also shown.
We deal with the bistable reaction-diffusion equation in an infinite star graph, which consists of several half-lines with a common end point. The aim of our study is to show the existence of front-like entire solutions together with the asymptotic behaviors as \begin{document}$ t\to\pm\infty $\end{document} and classify the entire solutions according to their behaviors, where an entire solution is meant by a classical solution defined for all \begin{document}$ t\in(-\infty, \infty) $\end{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.