The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in R2.We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior.Then,by employing the comparison principle and upper and lower solutions technique,we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation.We also obtain some similar results in R.
This paper is concerned with entire solutions ( t ∈ R) for bistable reaction-advection-diffusion equations in heterogeneous media. By using traveling curved fronts connecting a constant unstable stationary state and a stable stationary state, we proved that there exist entire solutions behaving as two traveling curved fronts coming from opposite directions, and approaching each other. Furthermore, we prove that such an entire solution is unique and Liapunov stable. The key technique is to characterize the asymptotic behavior of solutions at infinity in term of appropriate subsolutions and supersolutions.
