## On the time continuity of entropy solutions.(English)Zbl 1232.35029

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

### MSC:

 35B65 Smoothness and regularity of solutions to PDEs 35K65 Degenerate parabolic equations 35L65 Hyperbolic conservation laws
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### References:

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