Strong Time Periodic Solutions to the Bidomain Equations with FitzHugh-Nagumo Type Nonlinearities

TL;DR

This paper proves the existence and uniqueness of strong T-periodic solutions to the bidomain equations with FitzHugh-Nagumo type nonlinearities, using a novel periodic maximal regularity approach.

Contribution

It introduces a new periodic version of the Da Prato-Grisvard theorem to establish solutions for the bidomain equations with nonlinear ionic transport models.

Findings

Existence of unique strong T-periodic solutions

Application of a new periodic maximal regularity theorem

Results hold for models like FitzHugh-Nagumo, Aliev-Panfilov, Rogers-McCulloch

Abstract

Consider the bidomain equations subject to ionic transport described by the models of FitzHugh-Nagumo, Aliev-Panfilov, or Rogers-McCulloch. It is proved that this set of equations admits a unique, strong T-periodic solution provided it is innervated by T-periodic intra- and extracellular currents. The approach relies on a new periodic version of the classical Da Prato-Grisvard theorem on maximal L^p-regularity in real interpolation spaces.