Global stability of wavefronts with minimal speeds for nonlocal dispersal equations with degenerate nonlinearity (Q640184)

This article establishes the global exponential stability of the monostable traveling wave with the minimal speed for the nonlocal dispersal equation \[ u_t=J\ast u-u+f(u), \] where the nonlinearity \(f\) is degenerate in the sense that \(f'(0)=0\). To prove the result, the author carefully constructs a family of upper and lower solutions, then employs the squeezing technique, which was developed by \textit{X. Chen }[Adv. Differ. Equ. 2, No. 1, 125--160 (1997; Zbl 1023.35513)] for bistable waves and refined in several studies on monostable waves, to obtain the global stability up to the phase shift.