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

Ozkar Hernández Montero, Andrés Fraguela Collar, Raúl Felipe Sosa

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

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DOI: https://doi.org/10.21640/ns.v10i21.1531

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