The asymptotic behavior of a doubly nonlinear parabolic equation with a absorption term related to the gradient

By comparing the solution u(x, t) of the doubly degenerate parabolic equation ut = div(| Dum |p-2 Dum) - uq1 | ∇um |p1 with the Barenblatt type solution of the equation ut = div(| Dum |p-2 Dum), the large time asymptotic behavior of u(x, t) are got. Here the exponents m, p, p1 and q1 satisfy p > p1, p > 1,m > 1, q1 + p1m > m(p - 1) > 1.

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