Renormalized solutions of nonlinear parabolic equations with general measure data

Let $\mathrm{\Omega }\subseteq {\mathbb{R}}^N$ a bounded open set, $N\ge 2$, and let $p>1$; we prove existence of a renormalized solution for parabolic problems whose model is $$\{\begin{array}{ll}{u}_t-{\mathrm{\Delta }}_{p}u=\mu & \text{in }(0,T)\times \mathrm{\Omega },\\ u(0,x)=u_0& \text{in }\mathrm{\Omega },\\ u(t,x)=0& \text{on }(0,T)\times \mathrm{\partial }\mathrm{\Omega },\end{array}$$ where $T>0$ is any positive constant, $\mu \in M(Q)$ is a any measure with bounded variation over $Q=(0,T)\times \mathrm{\Omega }$, and $u_o\in L^1(\mathrm{\Omega })$, and $-\Delta_{p} u=-{\rm div} (|\nabla u|^{p-2}\nabla u )$istheusual$p$-laplacian.