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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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