On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown (Q338451)

The authors study the Cauchy problem for a multi-dimensional scalar balance law \( \partial_t u+\operatorname{div}\mathbf{F}(u)=G(u) \) with generally discontinuous flux vector \(\mathbf{F}(u)\) and source function \(G(u)\). Using an appropriate continuous re-parametrization of the graphs of \(\mathbf{F}(u)\) and \(G(u)\), they introduce the kinetic formulation of the problem and establish existence and uniqueness (under some additional requirements) of weak entropy solutions.