Transition Fronts in Time Heterogeneous and Random Media of Ignition Type

The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous media admit transition fronts or generalized traveling wave solutions with time dependent profiles and that such equations in time random media admit generalized traveling wave solutions with random profiles. Important properties of generalized traveling wave solutions, including the boundedness of propagation speeds and the uniform decaying estimates of the propagation fronts, are also obtained.