Submitted Paper

Inserted: 6 nov 2022
Last Updated: 6 nov 2022

Pages: 61
Year: 2022

Abstract:

Traveling waves are commonly observed in evolution systems. Such waves are robust in the sense that they are stable and exist for a wide range of parameters. Through $\Gamma$-convergence analysis, a well-known tool for studying concentration phenomena, a geometric variational problem representing the $\Gamma$-limit of a FitzHugh-Nagumo system in two dimensional domains is studied; this yields both the wave speed and the structure of a minimizer. In particular we demonstrate that 1D traveling fronts can become unstable when subject to 2D perturbation. In suitable parameter regimes multiple traveling waves, including non-planar structures, can co-exist. Stationary waves have been studied using geometric variational problems; ours represent the first attempt to treat non-stationary wave problems in multi-dimensional domains.

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