NDSU Applied Mathematics Seminar - Spring 2010
Loyola University Chicago
Department of Mathematics and Statistics


Time: 4:00PM-4:50PM  
BVM Hall - Room 1102 (6349 N. Kenmore Avenue, Chicago, IL 60626) [map]

Organizers: Marian Bocea and Rafal Goebel

Fall 2014 Analysis Seminar
Fall 2013 Analysis Seminar
Spring 2013 Analysis Seminar
Fall 2012 Analysis Seminar
Spring 2012 Analysis Seminar
Fall 2011 Analysis Seminar


MARCH 2015
Tuesday, March 10 - RAFAL GOEBEL (Loyola University Chicago) - Brockett's necessary condition for asymptotic stability and controllability
Abstract: If the origin is an asymptotically stable equilibrium for a differential equation dx/dt=f(x) with smooth enough right-hand side, then the image of any neighborhood of the origin under f contains a neighborhood of the origin. In particular, the vector field given by f takes on all directions on any neighborhood of the origin. Proofs of this result involve fixed point arguments, degree theory, converse Lyapunov results, etc. The talk will outline the proofs and include some motivation and examples.

Tuesday, March 31 - ROBERT JENSEN (Loyola University Chicago) - An alternate approach to the strong maximum principle
Abstract: I will describe a somewhat geometrical proof of the strong maximum principle.  By modifying this method I will recover a result of Y. Yu on the the norm of the gradient for $C^2$ solutions of the infinity Laplacian and indicate how to generalize this to similar operators.

APRIL 2015
Tuesday, April 7 - RAFAL GOEBEL (Loyola University Chicago) -  Steepest descent and nonlinear oscillator with damping (part I)
Abstract: What happens when you put a heavy ball on top of the graph of a smooth function? How does convexity of the function or friction affect the asymptotic behavior of the ball? What if the ball is replaced by a drop of liquid which slides in the steepest downhill direction? What does all this have to do with finding a minimum of a function? The talks will attempt to answer some of this questions... or at least formulate them properly. The first talk will focus on the continuous-time steepest descent (drop of liquid), the second on the nonlinear oscillator (heavy ball). Both talks are expository and non-expert friendly.

Tuesday, April 14 -
RAFAL GOEBEL (Loyola University Chicago) - Steepest descent and nonlinear oscillator with damping (part II)

Tuesday, April 21 -