Bendixson conditions for differential equations in Banach spaces

Series: 
CDSNS Colloquium
Monday, August 24, 2009 - 16:30
2 hours
Location: 
Skiles 255
,  
School of Mathematics, Georgia Tech
Organizer: 
The Bendixson conditions for general nonlinear differential equations in Banach spaces are developed in terms of stability of associated compound differential equations. The generalized Bendixson criterion states that, if some measure of 2-dimensional surface area tends to zero with time, then there are no closed curves that are left invariant by the dynamics. In particular, there are no nontrivial periodic orbits, homoclinic loops or heteroclinic loops. Concrete conditions that preclude the existence of periodic solutions for a parabolic PDE will be given. This is joint work with Professor James S. Muldowney at University of Alberta.