On the time continuity of entropy solutions

Clément Cancès, Thierry Gallouet

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