The minimal propagation speed of travelling waves for autocatalytic reaction-diffusion equations

This paper proves the existence of travelling waves for autocatalytic react ion-diffusion systems of a non-diffusive reactant and a diffusive autocatal yst where quadratic and cubic autocatalyses occur concurrently with the rat io 1 : k. We give the estimate of the minimal speed of travelling waves whi ch is consistent with the result obtaind by S. Focant and Th. Gallay for th e systems where a reactant and an autocatalyst are both diffusive. We furth er discuss the value of the parameter k which assures the validity of the h euristic argument employed by J. Murray and others.