Existence of global solutions in a model of electrical activity of the monodomain type for a ventricle

Abstract

Introduction: A monodomain model of electrical activity for an isolated ventricle is formulated. This model is written as a reaction diffusion PDE coupled to an ODE, The Rogers-Mculloch model is used to represent the electrical activity through the cell membrane. Method: We give a definition of weak and strong solution of the variational Cauchy problem associated to the monodomain model. A sequence of approximate solutions of Faedo-Galerkin type is proposed. Results: It is shown that the sequence of approximate solutions converge to a weak solution according to the proposed definition. Finally, we have that this weak solution is also a strong solution. Conclusion: The monodomain model of electrical activity in an isolated ventricle that is proposed has a weak solution in an appropriate sense. In addition, this weak solution is also a strong solution.

Keywords

• monodomain
• bidomain
• reaction-diffusion
• Faedo-Galerkin
• Rogers-Mculloch model
• electrical activity