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@ARTICLE{,
            author = {Bul{\'{\i}}{\v c}ek, Miroslav and Gwiazda, Piotr and {\'{S}}wierczewska-Gwiazda, Agnieszka},
             title = {On unified theory for scalar conservation laws with fluxes and sources being discontinuous with respect to the unknown},
           journal = {Journal of Differential Equations},
            volume = {262},
            number = {1},
              year = {2017},
             pages = {313--364},
               doi = {10.1016/j.jde.2016.09.020},
          abstract = {We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a kinetic formulation for the considered problem. To handle the discontinuities we work in the framework of re-parametrization of the flux and the source functions, which was previously used for Kružkov entropy solutions. Within this approach we obtain a fairly complete picture: existence of entropy measure valued solutions, entropy weak solutions and their equivalence to the kinetic solution. The results of existence and uniqueness follow under the assumption of H{\"{o}}lder continuity at zero of the flux. The source term, what is another novelty for the studies on problems with discontinuous flux, is only assumed to be one-side Lipschitz, not necessarily monotone function.},
  Preprint project = {MORE},
     Preprint year = {2016},
   Preprint number = {15},
       Preprint ID = {MORE/2016/15}
}