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 equation u t = div ( | D u m | p − 2 D u m ) − | D u m | p 1 − u q with initial condition u ( x , 0 ) = u 0 ( x ) . Here the exponents m, p, p 1 , q satisfy p > p 1 > p − 1 , q > m ( p − 1 ) > 1 , p > 1 , m > 1 .