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This paper is devoted to reaction-diffusion equations with bistablenonlinearities depending periodically on time. These equations admit twolinearly stable states. However, the reaction terms may not be bistable atevery time. These may well be a periodic combination of standard bistable andmonostable nonlinearities. We are interested in a particular class ofsolutions, namely pulsating fronts. We prove the existence of such solutions inthe case of small time periods of the nonlinearity and in the case of smallperturbations of a nonlinearity for which we know there exist pulsating fronts.We also study uniqueness, monotonicity and stability of pulsating fronts.

Pulsating fronts for bistable on average reaction-diffusion equations in a time periodic environment