Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness

Graziano Crasta (1) , Virginia de Cicco (1) , Guido de Philippis (2) , Francesco Ghiraldin (3)

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
3 UZH - Universität Zürich [Zürich] = University of Zurich

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.

Domains: Mathematics [math]; Analysis of PDEs [math.AP]

Graziano Crasta, Virginia de Cicco, Guido de Philippis, Francesco Ghiraldin. Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness. Archive for Rational Mechanics and Analysis, 2016, 221, pp.961 - 985. ⟨10.1007/s00205-016-0976-0⟩. ⟨ensl-01413640⟩