K-P-P-TYPE ASYMPTOTICS FOR NONLINEAR DIFFUSION IN A LARGE BALL WITH INFINITE BOUNDARY DATA AND ON R(D) WITH INFINITE INITIAL DATA OUTSIDE ALARGE BALL

Let u(n)(x,t) denote the minimal positive solution of u(t) = D/2 Delta u + u-u(2) in {x is an element of R(d): \x\ < n} x (0,infinity) u(x,0 ) = 0, \x\ < n, lim/\x\-->n u(x,t) = infinity, t > 0 and let U-n(x,t) denote the minimal positive solution of U-t = D/2 Delta U + U-U-2 in R (d) x (0,infinity) U(x,0) = 0, \x\ < n; U(x,0) = infinity, \x\ > n. Ex istence and upper and lower bounds are proven for u(n) and U-n. In par ticular, the bounds reveal the following characteristic K-P-P-type asy mptotics: Let {x(n)}(infinity)(n=1) subset of R(d) and {t(n)}(infinity )(n=1) subset of R(+). If lim/n-->infinity (n-\x(n)\) = infinity, then lim/n-->infinity u(n)(x(n),t(n)) = [GRAPHICS] If lim/n-->infinity t(n ) = infinity, then lim/n-->infinity U-n(x(n),t(n)) = [GRAPHICS]