Renormalised solutions of nonlinear parabolic problems with L1 data:: existence and uniqueness

In this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problem [GRAPHICS] where the data f and u(0) belong to L-1(Omega x (0, T)) and L-1(Omega), and where the function a:(0, T) x Omega x R-N --> R-N is monotone (but not necessarily strictly monotone) and defines a bounded coercive continuous operator from the space L-p(0, T; W-0(1,p)(Omega)) into its dual space. The renormalised solution is an element of C-0([0, T]; L-1(Omega)) such that its truncates T-K(u) belong to L-p(0, T; W-0(1,p)(Omega)) with [GRAPHICS] this solution satisfies the equation formally obtained jy using in the equation the test function S(u)phi, where phi belongs to c(0)(infinity)(Q) and where S belongs to C-infinity(R) with S' is an element of C-0(infinity)(R).