Renormalized Solution for the Nonlinear Parabolic Problem with Lower Order Terms

In this paper, we consider the following problem: $$\{\begin{array}{lll}-\mathrm{\nabla }\cdot A(x,u,\mathrm{\nabla }u)+H(x,u,\mathrm{\nabla }u)=f(x),& x\in \mathrm{\Omega },u=0,& x\in \mathrm{\partial }\mathrm{\Omega },\end{array}$$ in a bounded open set $\mathrm{\Omega }\subset {\mathbb{R}}^N$. We have established certain gradient estimates and proved the existence of a renormalized solution for the equation.