Stationary and traveling waves of the FitzHugh-Nagumo Equations
Time and place
12:30 PM on Thursday, March 21st, 2019; NAC 6/114
Yung Choi (U. Conn)
Abstract
The talk will be structured for general colloquium audience.
Stationary waves are steady state solutions in unbounded domain, while traveling waves will appear steady when viewed in a moving frame. We start with stationary waves of a scalar reaction-diffusion equation, as they can be easily explained using a phase plane analysis. Next we survey some results on the FitzHugh-Nagumo system. For some special parameter regimes, the solutions give discontinuous jump profiles as a certain parameter epsilon goes to zero. This can be analyzed using Γ-convergence and gives rise to a geometric variational problem; its radially symmetric solutions (known as bubbles) and their local stability are completely classified for all parameters.
We next turn our attention to traveling waves. Again we start with a scalar equation and work towards the FitzHugh-Nagumo systems. The use of a Γ-convergence analysis to traveling wave has recently been achieved. It seems to be the first instance of extending this kind of analysis to non-stationary problems.
