JournalsaihpcVol. 36, No. 2pp. 505–521

Regularity of solutions to scalar conservation laws with a force

  • Xavier Lamy

    Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, F-31062 Toulouse Cedex 9, France

  • Benjamin Gess

    Max-Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
Regularity of solutions to scalar conservation laws with a force cover
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Abstract

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.

Cite this article

Xavier Lamy, Benjamin Gess, Regularity of solutions to scalar conservation laws with a force. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 505–521

DOI 10.1016/J.ANIHPC.2018.07.002