Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness

Francesco Ghiraldin; Graziano Crasta; Guido De Philippis; Virginia De Cicco

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Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness

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arxiv 1509.08273 v2 pith:54XQOWCH submitted 2015-09-28 math.AP

Graziano Crasta , Virginia De Cicco , Guido De Philippis , Francesco Ghiraldin This is my paper

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keywords solutionsfluxapplicationsconservationdiscontinuouslawsstructureuniqueness

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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.

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