Asymptotic behaviour of solutions of a degenerate parabolic equation

The asymptotic behavior of nonnegative solutions of the following equations: ut = δpu - |u|q-1u in Q = RN × (0,∞), u(x,0) = φ(x), was studied where δpu=div(|∇u|p-2∇u), with p > 2N/(N + 1), N ≥ 1, max {1, p-1} < q < p - 1 + p/N and φ is a given nonnegative initial function. The long time behavior of nonnegative solutions is classified by a class of solutions with self-similarity depending on the parameters p,q and the asymptotic behavior of φ(x) as |x| → ∞.