Existence of a solution for a class of parabolic equations with three unbounded nonlinearities

We give an existence result of a renormalized solution for a class of nonlinear parabolic equations where the right-hand side belongs to L¹((0,T) × Ω) and where b(x, u) is an unbounded function of u and where −div(a(t, x, u, ∇u) + Φ(u)) is a Leray-Lions type operator with growth |∇u|^p−1 in ∇u, but without any growth assumption on u.