Regularity of solutions to scalar conservation laws with a force

Benjamin Gess (1) , Xavier Lamy (2)

1 MPI-MiS - Max Planck Institute for Mathematics in the Sciences
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove regularity estimates for entropy solutions to scalar conservation laws with a force. Based on the kinetic form of a scalar conservation law, a new decomposition of entropy solutions is introduced, by means of a decomposition in the velocity variable, adapted to the non-degeneracy properties of the flux function. This allows a finer control of the degeneracy behavior of the flux. In addition, this decomposition allows to make use of the fact that the entropy dissipation measure has locally finite singular moments. Based on these observations, improved regularity estimates for entropy solutions to (forced) scalar conservation laws are obtained.

Domaines: Equations aux dérivées partielles [math.AP]

Benjamin Gess, Xavier Lamy. Regularity of solutions to scalar conservation laws with a force. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, In press, ⟨10.1016/j.anihpc.2018.07.002⟩. ⟨hal-01591224⟩