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We deal with the Cauchy problem for multi-dimensional scalar conservationlaws, where the fluxes and the source terms can be discontinuous functions ofthe unknown. The main novelty of the paper is the introduction of a~kineticformulation for the considered problem. To handle the discontinuities we workin the framework of re-parametrization of the flux and the source functions,which was previously used for Kru\v{z}kov entropy solutions. Within thisapproach we obtain a fairly complete picture: existence of entropy measurevalued solutions, entropy weak solutions and their equivalence to the kineticsolution. The results of existence and uniqueness follow under the assumptionof H\"{o}lder continuity at zero of the flux. The source term, what is anothernovelty for the studies on problems with discontinuous flux, is only assumed tobe one-side Lipschitz, not necessarily monotone function.

On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown