Uniform bounds and asymptotic behavior for nonlinear parabolic equations with absorption terms

In this paper, we study the existence, the uniqueness and the behavior in time of global (in time) solutions of nonlinear parabolic equations of p-Lplacian type with absorption terms. Both of singular (fast diffusion) or degenerate problems (slow diffusion) will be considered. We show that the absorption terms of power type produces the existence and uniqueness of solutions with an improvement of the gradient regularity and universal bounds, which shows that all the solutions have exactly the same behavior in time, independently of their initial datum. The special autonomous case is also discussed.