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

@article{Giga2018StrongTS,
  title={Strong time-periodic solutions to the bidomain equations with arbitrary large forces},
  author={Yoshikazu Giga and Naoto Kajiwara and Klaus Kress},
  journal={Nonlinear Analysis: Real World Applications},
  year={2018}
}

The periodic version of the Da Prato–Grisvard theorem and applications to the bidomain equations with FitzHugh–Nagumo transport

In this article, the periodic version of the classical Da Prato–Grisvard theorem on maximal $${{L}}^p$$ L p -regularity in real interpolation spaces is developed, as well as its extension to

Time-Periodic Solutions to Bidomain, Chemotaxis-Fluid, and Q-Tensor Models

The main objective of this thesis is the investigation of different models arising from mathematical biology and fluid mechanics in the time-periodic setting. We consider the classical Keller-Segel

Existence of a T $T$ -Periodic Solution for the Monodomain Model Corresponding to an Isolated Ventricle Due to Ionic-Diffusive Relations

In this paper, we find relations between the ionic parameters and the diffusion parameters which are sufficient to ensure the existence of a periodic solution for a well-known monodomain model in a

The periodic version of the Da Prato–Grisvard theorem and applications to the bidomain equations with FitzHugh–Nagumo transport

In this article, the periodic version of the classical Da Prato–Grisvard theorem on maximal Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}

Asymptotic behavior of fronts and pulses of the bidomain model

The bidomain model is investigated in two spatial dimension and it is found that, after the planar front is destabilized, a rotating zigzag front develops whose shape can be explained by simple geometric arguments using a suitable Frank diagram.

References

SHOWING 1-10 OF 22 REFERENCES

Strong time-periodic solutions to the 3D primitive equations subject to arbitrary large forces

We show that the three-dimensional primitive equations admit a strong time-periodic solution of period 0$ ?>T>0, provided the forcing term f∈L2(0,T;L2(Ω)) is a time-periodic function of the same

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,

Optimal control of the bidomain system (II): uniqueness and regularity theorems for weak solutions

Motivated by the study of related optimal control problems, weak and strong solution concepts for the bidomain system together with two-variable ionic models are analyzed. A key ingredient for the

The bidomain problem as a gradient system

On the bidomain problem with FitzHugh–Nagumo transport

The bidomain problem with FitzHugh–Nagumo transport is studied in the $$L_p\!-\!L_q$$Lp-Lq-framework. Reformulating the problem as a semilinear evolution equation, local well-posedness is proved in

Stability of Front Solutions of the Bidomain Equation

The bidomain model is the standard model describing electrical activity of the heart. Here we study the stability of planar front solutions of the bidomain equation with a bistable nonlinearity (the

A collocation-Galerkin finite element model of cardiac action potential propagation

The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.