7 Lectures:

Week 1: June 15(Wed), 16(Thur), 9:00am-11:00am

Week 2: June 20(Mon), 3:00pm-5:00pm; 22(Wed), 23(Thur), 9:00am-11:00am

Week 3: June 27(Mon), 3:00pm-5:00pm; 29(Wed), 9:00am-11:00am

Tencent Meeting: 511-1367-6532 for 5 morning lectures

                         380-7490-8905 for 2 afternoon lectures 

This short course is suitable for graduate students who have some basic knowledge on ODEs (existence and uniqueness, asymptotic behavior, phase-plane analysis) and analytic semigroup theory for parabolic equations (well-posedness, spectrum).

Abstract:

In this short course, we shall first briefly introduce some basic theories and classical results on the existence and spatial decay of the planar traveling waves for three types of reaction diffusion models (bi-stable equation, Fisher’s equation and degenerate Fisher’s equation), which include the application of shooting methods and ODE asymptotic estimates and comparison method. Based on the known existence results, this course will focus on the introduction of the classical stability theories of planar traveling waves and the related theories and application of spectral analysis, especially the application of spectral analysis and the Evans function theories in three types reaction diffusion equations and some reaction diffusion systems.

Main topics in the short course:

1. Existence and spatial decay of traveling waves (2 lectures, 4 hours)

1) Application of shooting method and comparison method in bistable equation and Fisher equation

2) Application of shooting method and ODE asymptotic theories in degenerate Fisher equation

2. Introduction of stability theories of traveling waves and application classical spectral methods (5 lectures, 10 hours)

1) Introduction on the semigroup stability theories and stability theories of traveling waves (3 hours)

2) Introduction on the classical spectral theories and asymptotic stability of waves for some RD models (3 hours)

3) Introduction and application of Evans function method (4 hours)

Contact: Linlin Su (苏琳琳) sull@sustech.edu.cn