L-1 decay properties for a semilinear parabolic system

This article is concerned with the decay property in the L-1 norm as t --> infinity of the nonnegative solutions of the initial value problem in R-n { u(t) = Deltau + u \ delv \ (q) v(t) = Deltav + v \ delu \ (P) for different values of the parameters p, q greater than or equal to 1 and when mu, v < 0. If pq > (inf(p,q))/(n=1) + (n + 2)/(n + 1) then lim(t -->+infinity) \ \u(t) + v(t)\ \ (lambda) > 0 and when p,g < (inf(p,q))/(n+1) + (n + 2)/(n + 1) then lim(t<right arrow>+infinity) \ \u(t) + v(t)\ \ (1) = 0.