J. P. Keener, Homogenization and Propagation in the Bistable Equation, Physica D 136, 1-17 (2000).

Abstract:

We show that the standard method to homogenize inhomogeneous resistivity fails to give correct predictions about propagation speed and propagation failure when applied to the bistable equation. This shortcoming can be overcome with a more careful look at the averaging theorem. Using a generalized technique, we find an expression for the speed of waves that properly predicts propagation failure due to inhomogeneities.

J. P. Keener, Propagation of Calcium Waves in a Medium with Discrete Release Sites, SIAM J. Appl. Math. 61, 317-334 (2000).

Abstract:

We use averaging and homogenization techniques to study the propagation and propagation failure of calcium waves in cardiac cells where release of calcium is from discrete release sites. We derive analytical expressions for the waveform and for the speed of propagation to show the transition between continuous and "saltatory" propagation, and the transition between propagation success and its failure.