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

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.