This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlinear Halana...This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlinear Halanay's inequality, we prove that all noncritical traveling waves(waves with speeds c > c_*, c_* is minimal speed) are time-exponentially stable, when the initial perturbations around the waves are small. As a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11401478)
文摘This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlinear Halanay's inequality, we prove that all noncritical traveling waves(waves with speeds c > c_*, c_* is minimal speed) are time-exponentially stable, when the initial perturbations around the waves are small. As a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves.
