In this paper, we consider the multidimensional stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term in n–dimensional space. It is proved that, all planar traveling waves with speed c > c* are exponentially stable in the form of t−n/2e−ϵτσt, where constant σ > 0 and ϵτ = ϵ(τ ) ∈ (0, 1) is a decreasing function for the time delay τ > 0. While, for the planar traveling waves with speed c = c*, we prove that they are algebraically stable in the form of t−n/2. The Fourier transform plays a crucial role in transforming the competition systems to a linear delayed differential system. We establish the comparison principle and some estimates in weighted spaces L1w(Rn) and Ww2,1(Rn) to obtain the main results.
In this paper, we consider the multidimensional stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term in n-dimensional space. It is proved that, all planar traveling waves with speed c > c * are exponentially stable in the form of t − n 2 e −ϵτ σt , where constant σ > 0 and ϵ τ = ϵ(τ ) ∈ (0, 1) is a decreasing function for the time delay τ > 0. While, for the planar traveling waves with speed c = c * , we prove that they are algebraically stable in the form of t − n 2 . The Fourier transform plays a crucial role in transforming the competition systems to a linear delayed differential system. We establish the comparison principle and some estimates in weighted spaces L 1 w (R n ) and W 2,1 w (R n ) to obtain the main results.
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