14:00 - 15:00, February 19, 2025 (Wednesday) Room 515, Cosmology Building, NTU
(臺灣大學次震宇宙館 515研討室)
The Non-Monotone Waves in the Two-Species Lotka-Volterra Competition Model Shun-Chieh Wang (NCTS)
Abstract
We investigate the Lotka–Volterra competitive reaction-diffusion equation with a focus on the coexistence phenomenon. To understand the system's dynamics, it is essential to investigate traveling wave solutions.
Our primary interest lies in the solutions connecting the two equilibria and . We consider the following system
where
Previous studies have established the existence of strictly monotone solution; however, the solution is not unique.
In this work, we reprove the existence of such solution using Schauder's fixed-point theorem. Through this method, we successfully construct a non-monotone traveling wave solution under specific coefficients. This shows the non-uniqueness of the solutions.
If time permits, we will also discuss the stability of these solutions.
