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Applied Analysis
Seminar information archive ～06/11｜Next seminar｜Future seminars 06/12～
| Date, time & place | Thursday 16:00 - 17:30 Room # (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kazuhiro Ishige, Yasuhito Miyamoto, Neal Bez, Ryo Takada |
2026/06/25
16:00-17:30 Room # 002 (Graduate School of Math. Sci. Bldg.)
Xiao Dongyuan (Tohoku University)
Complete classification of traveling wave solutions to monotone dynamical systems (Japanese)
Xiao Dongyuan (Tohoku University)
Complete classification of traveling wave solutions to monotone dynamical systems (Japanese)
[ Abstract ]
To study the propagation phenomena of solutions to the reaction-diffusion equation the asymptotic behavior of traveling wave solutions plays a crucial role. When the nonlinear reaction term satisfies the monostable condition, it is known that there exists a minimal traveling wave speed, and that traveling wave solutions exist for any speed c larger than or equal to the minimal speed. It has been shown, through simple phase plane analysis, that these traveling waves can be classified into three cases based on their decay rates.
It Is expected that a similar classification should hold for more general order-preserving systems, such as nonlocal diffusion equations, Lotka–Volterra systems, and reaction–diffusion equations with time delay. However, a complete classification remains unavailable because direct phase plane analysis is no longer applicable in these settings. In this talk, I will introduce a method based on comparison argument and sliding method to classify traveling waves. This research is based on joint work with Maolin Zhou (Nankai University) and Chang-hong Wu (National Yang Ming Chiao Tung University).
To study the propagation phenomena of solutions to the reaction-diffusion equation the asymptotic behavior of traveling wave solutions plays a crucial role. When the nonlinear reaction term satisfies the monostable condition, it is known that there exists a minimal traveling wave speed, and that traveling wave solutions exist for any speed c larger than or equal to the minimal speed. It has been shown, through simple phase plane analysis, that these traveling waves can be classified into three cases based on their decay rates.
It Is expected that a similar classification should hold for more general order-preserving systems, such as nonlocal diffusion equations, Lotka–Volterra systems, and reaction–diffusion equations with time delay. However, a complete classification remains unavailable because direct phase plane analysis is no longer applicable in these settings. In this talk, I will introduce a method based on comparison argument and sliding method to classify traveling waves. This research is based on joint work with Maolin Zhou (Nankai University) and Chang-hong Wu (National Yang Ming Chiao Tung University).
