Finer regularity of an entropy solution for 1-d scalar conservation laws with non uniform convex flux
Karthik AdimurthiTata Institute of Fundamental Research, Bangalore, India
Shyam Sundar GhoshalUniversité de Franche-Comté, Besançon, France
G.D. Veerappa GowdaTata Institute of Fundamental Research, Bangalore, India
Consider a scalar conservation law in one space dimension with initial data in If the flux is in and locally uniformly convex, then for all , the entropy solution is locally in BV (functions of bounded variation) in space variable. In this case it was shown in , that for all most every , locally, the solution is in SBV (Special functions of bounded variations). Furthermore it was shown with an example that for almost everywhere in cannot be removed. This paper deals with the regularity of the entropy solutions of the strict convex flux which need not be in and locally uniformly convex. In this case, the entropy solution need not be locally in BV in space variable, but the composition with the derivative of the flux function is locally in BV. Here we prove that, this composition is locally is in SBV on all most every . Furthermore we show that this is optimal.
Cite this article
Karthik Adimurthi, Shyam Sundar Ghoshal, G.D. Veerappa Gowda, Finer regularity of an entropy solution for 1-d scalar conservation laws with non uniform convex flux. Rend. Sem. Mat. Univ. Padova 132 (2014), pp. 1–24DOI 10.4171/RSMUP/132-1