DYNAMICS OF INTERFACES IN COMPETITION-DIFFUSION SYSTEMS

This paper is competition-diffusion system concerned with the dynamics of interfaces in the Lotka-Volterra competition-diffusion system u(t) = epsilon(2) Delta u + u(1-u-cw), w(t) = epsilon(2)D Delta w + w(a - bu - w), in R(n), where epsilon > 0 is a small parameter and D > 0 is a constant. If 0 < 1/c < a < b, this system has two locally stable equ ilibria, (u,w) = (1,0) and (0, a). In this case, interfaces may appear that separate R(n) into two regions occupied by u and w, respectively . In this paper, it is shown that the normal velocity of the interface is approximately given by epsilon theta, which is equal to the propag ation speed of a traveling wave solution to the above system in one di mension. When theta = 0, it is shown that the normal velocity of the i nterface is approximately given by -epsilon(2)(n - 1)L(k)appa, where L > 0 is a weighted mean of 1 and D, and kappa is the mean curvature of the interface.