Uniqueness of the very singular solution of a degenerate parabolic equation

A quasilinear degenerate diffusion equation with absorption ut = δpu - |u|q-1u in Q = RN × (0,∞) (1.1), where δpu = div(|∇u|p-2∇u), with 2N/(N + 1) < p < 2, N ≥ 2, and 1 < q < p - 1 + p/N. A very singular solution W of (1.1) is a nonnegative continuous function in Q - {(0,0)} such that (1) W(x,0) = 0 for x ≠ 0; (2) ∇W ε Lloc1(0,∞ : Wloc1,p-1(RN)) and (1.1) is satisfied in the sense of distribution in Q; (3) ∫RN W(x,t)dx → ∞ as t → 0.