Entire solutions of time periodic bistable reaction-advection-diffusion equations in infinite cylinders

This paper is concerned with the existence and some qualitative properties of entire solutions for a reaction-advection-diffusion equation in infinite cylinders with time periodic bistable nonlinearity. Here, an entire solution means a solution defined in the whole space and for all time t is an element of R. By the comparison principle coupled with the supersolution and subsolution technique, it is proved that there exists an entire solution. Furthermore, it is shown that such an entire solution is unique and Liapunov stable. Unlike the reaction-diffusion equation without advection, the lack of symmetry between increasing and decreasing traveling fronts caused by the advection affects the construction of supersolutions and subsolutions. (C) 2015 AIP Publishing LLC.