Large time behavior of solutions to a class of doubly nonlinear parabolic equations

We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u _t = div(u ^m−1|Du| ^p−2 Du) − u ^q with an initial condition u(x, 0) = u ₀(x). Here the exponents m, p and q satisfy m + p ⩾ 3, p > 1 and q > m + p − 2. The paper was supported by NSF of China (10571144), NSF for youth of Fujian province in China (2005J037) and NSF of Jimei University in China.