Before revision:  In this paper, we investigate the instability and asymptotic behavior of planar fronts and planar pulses of the bidomain Allen--Cahn equation and the bidomain FitzHugh--Nagumo equation in two spatial dimension.
After revision:  In this paper, we investigate the instability and asymptotic behavior of planar fronts and planar pulses of the bidomain Allen--Cahn equation and the bidomain FitzHugh-Nagumo equation in two spatial dimension.