Existence, uniqueness and stability of forced waves for asymptotical KPP equations with the nonlocal dispersal in a shifting habitat

In this paper, we mainly focus on the existence, uniqueness and stability of forced waves for the asymptotical KPP equation with the nonlocal dispersal in a shifting habitat. Firstly, we adopt the monotone semiflow technique together with Dini's Theorem to obtain the existence of forced waves with the wave speed $ c $, which is a given speed of habitat edge movement. Next, we obtain the uniqueness of forced waves via the sliding method. Lastly, by using the monotone semiflows technique in conjunction with the upper-lower solutions, we first obtain the solution of initial problem uniformly converges to the forced wave, and further give the global exponential stability of the forced wave.