Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness
arXiv:1509.08273 · doi:10.1007/s00205-016-0976-0
Abstract
We investigate the structure of solutions of conservation laws with discontinuous flux under quite general assumption on the flux. We show that any entropy solution admits traces on the discontinuity set of the coefficients and we use this to prove the validity of a generalized Kato inequality for any pair of solutions. Applications to uniqueness of solutions are then given.
20 pages in Arch. Rational Mech. Anal. (2016) - online first