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Nova scientia
versión On-line ISSN 2007-0705
Resumen
HERNANDEZ MONTERO, Ozkar; FRAGUELA COLLAR, Andrés y SOSA, Raúl Felipe. Existence of global solutions in a model of electrical activity of the monodomain type for a ventricle. Nova scientia [online]. 2018, vol.10, n.21, pp.17-44. ISSN 2007-0705. https://doi.org/10.21640/ns.v10i21.1531.
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.
Palabras llave : monodomain; bidomain; reaction-diffusion; Faedo-Galerkin.
