Math 525
Ordinary Differential Equations II

Cab 575


Syllabus: LINK
Summary: In
this course we will study asymptotics of ordinary
differential equations and boundary value problems.
The PoincareBendixson theory has been covered in Math
524. We cover the theory of dynamical systems and
differential equations in Banach spaces. The concepts
of stability and bifurcations can be generalized from
ODEs to PDEs. We will systematically derive a
theory of finite dimensional compact global
attractors, and we will investigate two examples in
detail: the NavierStokes equations and
reactiondiffusion equations. Texts:


Lecture Notes 
Assignments due at 9 AM in
class:


1. Introduction 
We skip the following sections (1.5) (1.7) since they were covered in Math 524: 

2. Some Functional Analysis  
3. ReactionDiffusion Equations  
4. The Navier Stokes Equation  
5. Global Attractors  
6. Global Attractor for ReactionDiffusion Equations in 1D  
7. Global Attractor for NavierStokes Equations in 2D  
8. Finite
Dimensional Attractors
