Weinberger, H.F.2007-08-162007-08-161982https://hdl.handle.net/11299/5118The system ut = {(1 + v)}xx + (R1 - au - bv)u vt = (R2 - bu - av)v {(1 + u)}xx = 0 at x = 0 and x = 1 with 1/2 (a/b + b/a) < R1/R2 < a/b and > a(a2 - b2) / 2abR1 - (a2 + b2) R2 was considered by M. Mimura [2] as a model for the population densities of two competing species, one of which increases its migration rate in response to crowding by the other species. It is a special case of the model of N. Shigesada, K. Kawasaki, and E. Teramoto [3].