In this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problemwhere the d a t a / a n d u 0 belong to L l (Q x (0, T)) and L'(O), and where the function a:(0, T) x Q x R w -> R N is monotone (but not necessarily strictly monotone) and defines a bounded coercive continuous operator from the space i/(0, T; Wj' p (O)) into its dual space. The renormalised solution is an element of C°([0, T]; 1/(0)) such that its truncates T K (u) belong to L"(0, T, Wj' p (O)) with lim \Du\ p dxdt = 0; x~+ ™ JKSMSK + I this solution satisfies the equation formally obtained by using in the equation the test function S(u)
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