Résumé:
We investigate the following quasi-linear and singular parabolic equation ,
8><
>:
ut Δpu =
1
u + f(x; u) in QT ;
u = 0; on T ; u > 0 in QT ; (Pt)
u(0; x) = u0(x) in Ω:
WhereΩis an open bounded domain with smooth boundary inRN(withN 2), 1 < p < 1,
0 < , T > 0, QT = (0; T) Ω and T = (0; T) @Ω. We assume that f is bounded below
Caratheodory function and u0 2 W1;p
0 (Ω). In this memory we will study the existence and
uniqueness of the weak solution of (Pt) using method of semi- discretization in time and we
study the stabilization.