A reaction-diffusion system modeling the cardiac electric field
We are concerned with a degenerate system of nonlinear
equations modeling the cardiac electric field at macroscopic level.
First, the existence of weak solutions is proved via non degenerate
system, Faedo-Galerkin, monotonicity and compactness methods.
Second, we prove the existence of a weak solution by demonstrating that
the finite volume scheme
is convergent and that any limit function satisfies the definition of
weak solution. The convergence proof is based on deriving a series of a
and using a general $L^p$ compactness.
Mostafa Bendahmane (University of Oslo, Norway)
July 15, 2005