On the time continuity of entropy solutions

We show that any entropy solution $u$ of a convection diffusion equation ${\mathrm{\partial }}_{t}u+÷F(u)-\mathrm{\Delta }\varphi (u)=b$ in $\text{OT}$ belongs to $C([0,T),L_{Loc}^1(\text{o}\text{O}))$. The proof does not use the uniqueness of the solution.