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We study the existence of solutions of the nonlinear parabolic problem ∂u ∂t − div[|Du − Θ(u)| p−2 (Du − Θ(u))] + α(u) = f in ]0, T [ × Ω, (|Du − Θ(u)| p−2 (Du − Θ(u))) • η + γ(u) = g on ]0, T [ × ∂Ω, u(0, •) = u 0 in Ω, with initial data in L 1. We use a time discretization of the continuous problem by the Euler forward scheme.

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This work is devoted to study a doubly non linear elliptic-parabolic problem with quadratic gradient term by Rothe's method. We investigate the long time behavior of the solution to the discrete problem and prove the existence of compact global attractor. Our method relays on semi-discretization with respect to the time variable.

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