arXiv subjects

Klaus Kress

Publications and source records attributed to Klaus Kress.

2 recordsLinked to original sources

arXiv2018

Strong time-periodic solutions to the bidomain equations with arbitrary large forces

We prove the existence of strong time-periodic solutions to the bidomain equations with arbitrary large forces. We construct weak time-periodic solutions by a Galerkin method combined with Brouwer's fixed point theorem and a priori estimate independent of approximation. We then show their regularity so that our solution is a strong time-periodic solution in $L^2$ spaces. Our strategy is based on the weak-strong uniqueness method.

math.AP↗

arXiv2017

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

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.

math.AP↗