TY - JOUR
T1 - Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations
AU - Taniguchi, Masaharu
N1 - Funding Information:
Acknowledgments. This work is supported by JSPS Grant-in-Aid for Scientific Research (C) Grant Number 26400169.
Publisher Copyright:
© 2020 American Institute of Mathematical Sciences. All rights reserved.
PY - 2020
Y1 - 2020
N2 - For a balanced bistable reaction-diffusion equation, the existence of axisymmetric traveling fronts has been studied by Chen, Guo, Ninomiya, Hamel and Roquejoffre [4]. This paper gives another proof of the existence of axisymmetric traveling fronts. Our method is as follows. We use pyramidal traveling fronts for unbalanced reaction-diffusion equations, and take the balanced limit. Then we obtain axisymmetric traveling fronts in a balanced bistable reaction-diffusion equation. Since pyramidal traveling fronts have been studied in many equations or systems, our method might be applicable to study axisymmetric traveling fronts in these equations or systems.
AB - For a balanced bistable reaction-diffusion equation, the existence of axisymmetric traveling fronts has been studied by Chen, Guo, Ninomiya, Hamel and Roquejoffre [4]. This paper gives another proof of the existence of axisymmetric traveling fronts. Our method is as follows. We use pyramidal traveling fronts for unbalanced reaction-diffusion equations, and take the balanced limit. Then we obtain axisymmetric traveling fronts in a balanced bistable reaction-diffusion equation. Since pyramidal traveling fronts have been studied in many equations or systems, our method might be applicable to study axisymmetric traveling fronts in these equations or systems.
KW - Axisymmetric
KW - Balanced
KW - Reaction-diffusion equation
KW - Traveling front
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U2 - 10.3934/dcds.2020126
DO - 10.3934/dcds.2020126
M3 - Article
AN - SCOPUS:85082536287
SN - 1078-0947
VL - 40
SP - 3981
EP - 3995
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 6
ER -