Transition waves for a class of space-time dependent monostable equations

We investigate the existence of generalized transition waves for reaction-diffusion KPP equations depending explicitly on time and space. In the case of spatially periodic diffusion and drift, and general temporal dependence of the nonlinearity, we almost completely characterize the set of admissible speeds of the waves in terms of a suitable notion of mean introduced in [15]. A lower bound for the speeds is also derived for equations with non-periodic, spatially dependent coefficients, without assuming the KPP condition. © 2014 International Press.