Some analytical results on the Gray–Scott model

Abstract

We consider the Gray–Scott model for cubic autocatalysis. We prove nonexistence results on stationary and travelling pulse solutions for some domain of parameters. We obtain an explicit travelling front in the one dimensional case for equal diffusivities and equal transformation rates of the reactants. We prove that travelling fronts continue to exist near the equal diffusivities and equal transformation rates case. We also provide numerical simulations illustrating our results.