Extinction and decay estimates of solutions for a class of doubly degenerate equations

In this paper, we study the extinction and decay estimates under suitable L p -integral norm of solutions to the initial–boundary value problem for the fast diffusion doubly degenerate equation u t = div ( ∣ ∇ u m ∣ p − 2 ∇ u m ) + λ ∣ u ∣ q − 1 u − β u , where ( x , t ) ∈ Ω × ( 0 , + ∞ ) , 1 < p < 2 , 0 < m ( p − 1 ) ≤ q < 1 , λ > 0 , β > 0 , and Ω ⊂ R N is a bounded domain with smooth boundary.