On the FitzHugh - Nagumo Model

The initial value problem P, in all of the space, for the spatio - temporal FitzHugh - Nagumo equations is analyzed. When the reaction kinetics of the model can be outlined by means of piecewise linear approximations, then the solution of P is explicitly obtained. For periodic initial data are possible damped travelling waves and their speed of propagation is evaluated. The results imply applications also to the non linear case