Numerical approximation of reaction-diffusion problems in electrocardiology using probabilistic methods

Controllability of Degenerating Reaction-Diffusion System in Electrocardiology

This paper is devoted to analyze the null controllability of a nonlinear reaction-diffusion system approximating a parabolic-elliptic system modeling electrical activity in the heart. The uniform, with respect to the degenerating parameter, null controllability of the approximating system by a single control force acting on a subdomain is shown. The proof needs a precisely estimate with respect...

Numerical Methods for Stiff Reaction-diffusion Systems

In a previous study [21], a class of efficient semi-implicit schemes was developed for stiff reaction-diffusion systems. This method which treats linear diffusion terms exactly and nonlinear reaction terms implicitly has excellent stability properties, and its second-order version, with a name IIF2, is linearly unconditionally stable. In this paper, we present another linearly unconditionally s...

Numerical Methods for Power-Law Diffusion Problems

Numerical Methods for Solving Convection-Diffusion Problems

Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective transport of individual phases. Moreover, for compressible media, the pressure equation itself is just a time-dependent convection-diffusion equation. For differen...

Energy Methods for Reaction - Diffusion Problems

ENERGY METHODS FOR REACTION-DIFFUSION PROBLEMS by Xing Zhong Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. These kinds of questions were originally...