期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 267, 期 2, 页码 1247-1276出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2019.02.008
关键词
Reaction-diffusion equation; Bistable nonlinearity; Entire solution; Traveling wave; Front transition; Blocking of propagation
类别
资金
- JSPS KAKENHI [JP18H01139, JP16K05218, JP26247013]
There exists a traveling front wave to a bistable reaction-diffusion equation in a whole line under a certain condition of reaction term f (u). We deal with the bistable reaction-diffusion equation with the same f (u) in a domain St which is a graph of special type, that is, a union of half-lines starting at a common point, so the domain has a unique junction of the half-lines. The aim of our study is to show the existence of nontrivial entire solutions, which are classical solutions defined for all (x, t) is an element of Omega x R. We prove that there are entire solutions which converge to the front waves in some of half-lines and converge to zero in the remaining half-lines as t -> -infinity. We also give a condition under that the entire solutions exhibit the blocking of the front propagation. This blocking is caused by the emergence of stationary solutions. The stability/instability of the stationary solutions are proved. (C) 2019 Elsevier Inc. All rights reserved.
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