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)

Biography

吴雅萍，首都师范大学数学科学学院教授、博士生导师。主要从事非线性偏微分方程的理论研究工作，在对多种类型的反应扩散方程组解的定性研究，哈密顿系统的孤立波，以及抛物双曲耦合方程行波解的稳定性研究方面取得一系列创新性的研究成果, 曾先后主持了多项国家及省部级科研项目。
个人主页：https://math.cnu.edu.cn/szdw/qtjs/122250.htm

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