Wave speeds of density dependent Nagumo diffusion equations - inspired by oscillating gap-junction conductance in the islets of Langerhans

The equation ut = (D(u)ux)x + f(u) arises in several biological examples and is known to have wave solutions for appropriate D and f. We give here a new formula for finding an approximation to the wave speed, relevant for comparing experiments with model simulations. This is done in details for the simple example D(u) = u + k and an N-shaped f, derived from a model of coupled pancreatic beta-cells, where the coupling conductance follows the electrical activity as it is found in experiments. On the way, we claim that the wave speed does not depend on the parameter g(K,ATP), mimicking the glucose concentration in the islet, in sharp contrast to the claim set forth in the article by Aslanidi et al.