The spectral theory is a basic technique to study the stability of ODE or PDE solutions. The key is to find the essential spectrum. In this talk, I will follow paper [1] to introduce the basic technique which help us to characterize the essential spectrum, and prove the stability of TWS in 3 species competition model.

 

Reference:

[1] Chueh-Hsin Chang, The stability of traveling wave solutions for a diffusive competition system of three species. J.Math.Anal.Appl.459(2018) 564-576

[2] JS Guo, Y Wang, CH Wu, CC Wu, The minimal speed of traveling wave solutions for a diffusive three species competition system. Taiwan J.Math (2015)

[3] Kapitula Todd and Promislow Keith, Spectral and Dynamical Stability of Nonlinear Waves. Springer (2013)