COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION

In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption u(t) - Delta u(m) + gamma u(p) = 0, where gamma >= 0, m > 1 and p > m + 2/N. We will show that if gamma = 0 and 0 < mu < 2N/N(m-1)+2 , or gamma > 0 and 1/p-1 < mu < 2N/N(m-1)+2, then for any nonnegative function phi in a nonnegative countable subset F of the Schwartz space S(R-N), there exists an initial-value u(0) is an element of C(R-N) with lim u(0)(x) = 0 x ->infinity such that phi is an w-limit point of the resealed solutions t(mu/2)u(t(beta.),t) where beta = 2-mu(m-1)/4.