MULTIDIMENSIONAL STABILITY OF PLANAR TRAVELING WAVES FOR THE DELAYED NONLOCAL DISPERSAL COMPETITIVE LOTKA-VOLTERRA SYSTEM

In this paper, we consider the multidimensional stability of planar traveling waves for the nonlocal dispersal competitive Lotka-Volterra system with time delay in n-dimensional space. More precisely, we prove that all planar traveling waves with speed c > c* are exponentially stable in L-infinity(R-n) in the form of t(-n/2 alpha) e-epsilon(tau)sigma t some constants sigma > 0 and epsilon(tau) is an element of (0, 1), where epsilon(tau) = epsilon(tau) is a decreasing function refer to the time delay tau > 0. It is also realized that, the effect of time delay essentially causes the decay rate of the solution slowly down. While, for the planar traveling waves with speed c = c*, we show that they are algebraically stable in the form of The t-(n/2 alpha). adopted approach of proofs here is Fourier transform and the weighted energy method with a suitably selected weighted function.