STUDY GROUP

INTRODUCTION TO TRAVELING WAVES

Organizers: Anna Ghazaryan,  Milena Stanislavova

• Group Format: an informal group of faculty and students
• Purpose: introducing the basic knowledge in the area of traveling waves in various applications and related techniques
• Form of the meetings:  reviews, presentations, discussions,  computer lab sessions
• Topics: topics will be chosen  according to interests of the group members
• Pace: comfortable
  
• Activity levels:  every group member is expected to be actively involved
• Time and Location:  Monday 2:00pm,  456 Snow Hall
• Participants: Maila Brucal, Aslihan Demirkaya, Charles Lamb, Kacey Stertz
  

Tentative Schedule

1. Traveling waves: definitions, examples                      (01.26.2009)
   
2. Existence: examples of proof techniques                   (02.02.2009)
3. Introduction to Auto.                                                  (02.09.2009)
4. Homoclinic and heteroclinic orbits using AUTO       (02.16.2009)
5. Stability of  traveling waves                                       (02.23.2009)
6. Bifurcation theory; Auto: Hopf bifurcation               (02.02.2009)                                         
   
7. Evans function
8. Stability in weighted spaces
   
9. Nonlinear stability
10. Diffusive dynamics
    

Tentative (not complete) list of references and reading material:

• NUMERICS/AUTO
• E. Doedel. Lecture notes of numerical analysis of nonlinear equations   (available on  Doedel's homepage)
• XPPAUT by Bard Ermentrout
• Download AUTO

• P. Collet, J.P. Eckmann. Instabilities and Fronts in Extended Systems. 
  
• D. Henry. Geometric theory of semilinear parabolic equations.
  
• A. Pazy. Semigroups of linear operators and applications to partial differential operators.
• B. Sandstede. Stability of traveling waves.  "Handbook of Dynamical Systems II", 2002, p.983-1055.
• A. Mielke, G. Schneider, H. Uecker. Stability and Diffusive Dynamics on Extended Domains.