On the time continuity of entropy solutions

Abstract

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

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Correspondence to Clément Cancès.

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Cancès, C., Gallouët, T. On the time continuity of entropy solutions. J. Evol. Equ. 11, 43–55 (2011). https://doi.org/10.1007/s00028-010-0080-0

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Mathematics Subject Classification (2000)

  • 35L65
  • 35B65
  • 35K65

Keywords

  • Entropy solution
  • Time continuity
  • Scalar conservation laws