On the time continuity of entropy solutions

Clément Cancès (1) , Thierry Gallouët (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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

Mots clés: Entropy solution; time continuity; scalar conservation laws

Domaines: Equations aux dérivées partielles [math.AP]

Clément Cancès, Thierry Gallouët. On the time continuity of entropy solutions. Journal of Evolution Equations, 2011, 11 (1), pp.43-55. ⟨hal-00349222v2⟩