Stability of fronts of bidomain models

Time and location: June 9, 2022, 2:00 PM (Sydney time) at the University of New England 

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Title: Stability of fronts of bidomain models

Abstract:  Bidomain models are widely used to simulate electrical signal transmissions in the heart. Mathematically bidomain models are expressed in terms of pseudo-differential equations involving a Fourier integral operator that is anisotropic. Despite their importance in cardiac electrophysiology, systematic mathematical studies of bidomain models started only relatively recently.  As the bidomain models usually have strong anistropy, the stability of fronts depends on the direction of its motion.  In 2016, we considered bidomain Allen-Cahn type equations on R^2 and revealed the deep relation between the linear stability of a planar wave and the so-called Frank diagram (joint work with Yoichiro Mori, CPAM 2016).  In this talk, I will present our recent results on the nonlinear stability of a planar wave of bidomain Allen-Cahn type equations and also show some numerical simulations of pulse waves of the bidomain FitzHugh-Nagumo system that are noticeably different from those of the conventional FitzHugh-Nagumo systems. This is joint work with Yoichiro Mori, Mitsunori Nara and Koya Sakakibara. 

Miranda,
On Behalf of Daniel H.