The asymptotic behavior of solutions for a class of doubly degenerate nonlinear parabolic equations

By using the Morse interaction technique, supposing that the uniqueness of the Barenblatt-type solution is true, the paper studies the large time asymptotic behavior of solutions for the doubly degenerate parabolic equationut=div(|Dum|p−2Dum)−|Dump1|−uqut=div(|Dum|p−2Dum)−|Dum|p1−uq with initial condition u(x,0)=u0(x)u(x,0)=u0(x). Here the exponents m, p  , p1p1, q   satisfy p>p1>p−1p>p1>p−1, q>m(p−1)>1q>m(p−1)>1, p>1p>1, m>1m>1.