MULTI-DIMENSIONAL SCALAR CONSERVATION LAWS WITH FLUXES DISCONTINUOUS IN THE UNKNOWN AND THE SPATIAL VARIABLE
2013
Abstrakt
The paper deals with a scalar conservation law in an arbitrary dimension d with a discontinuous flux. The flux is supposed to be a discontinuous function in the spatial variable x and in an unknown function u.
Under some additional hypothesis on the structure of possible discontinuities, we formulate an appropriate notion of entropy solution and establish its existence and uniqueness. The framework for proving the existence and uniqueness of entropy weak solutions is provided by the studies on entropy measure-valued solutions and may be viewed as a corollary of the uniqueness theorem for entropy measure-valued solutions.