The Γ-limit of traveling waves in the FitzHugh-Nagumo system

Patterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems. A common theme in investigating such systems is to identify the intrinsic factors responsible for such self-organization. The Γ-convergence is a well-known technique applicable to variational formulations of concentration phenomena of stable patterns. Recently a geometric variational functional associated with the Γ-limit of standing waves of the FitzHugh-Nagumo system has been built. This article studies the Γ-limit of traveling waves. To the best of our knowledge, this is the first attempt to expand the scope of applicability of Γ-convergence to cover non-stationary problems.