Traveling waves in a three-variable reaction-diffusion-mechanics model of cardiac tissue.

In this paper, we study the existence and stability of traveling waves in a three-variable reaction-diffusion-mechanics system, which was derived by Matt Holzer, Arjen Doelman, and Tasso J. Kaper [15]. This system consists of a modified FitzHugh-Nagumo equation coupled with two elasticity equations. We provide the proof of existence of traveling pulses by using geometric singular perturbation theory and an exchange lemma. Then, we analyze the spectrum of linearized operators about traveling pulses by combining geometric singular perturbation theory and the Lin-Sandstede method, and we prove that the traveling pulse is spectrally stable. Precisely, we show that there is at most a nontrivial eigenvalue near the origin, which turns out to be negative. [ABSTRACT FROM AUTHOR]