Solutions to the Hodgkin-Huxley equations

摘要

An existence and uniqueness theorem for solutions to the Hodgkin-Huxley equations for the propagation of an electrical impulse in the case of a nerve of finite length is given. Moreover it is shown that the solutions are regular and depend continuously upon the data. Finally it is proved that if the nerve is sufficiently short, then in the absence of any impulse all solutions decay exponentially to equilibrium.