The asymptotic behavior of the solution of a doubly degenerate parabolic equation with the convection term

The objective of this article is to study the large time asymptotic behavior of the nonnegative weak solution of the following nonlinear parabolic equation ut = div(vertical bar Du(m)vertical bar(p-2)Du(m)) + div (B(u(m))) with initial condition u(x, 0) = u (0)(x). By using Moser iteration technique, assuming that the uniqueness of the Barenblatt-type solution E (c) of the equation u (t) = div(|Du (m) | (p-2) Du (m) ) is true, then the solution u may satisfy t(1/mu)vertical bar u(x, t) - E-c(x, t)vertical bar -> 0, as t -> infinity which is uniformly true on the sets {x is an element of R-N: vertical bar x vertical bar < at(1/mu N), a>0}. Here B(u(m) ) = (b(1)(u(m) ), b(2)(u(m) ), ..., b(N) (u(m))) satisfies some growth order conditions, the exponents m and p satisfy m(p - 1) > 1.