Abstract
The Riemann problem for a class of nonlinear systems of first order hyperbolic conservation laws is studied. The class consists of systems where the derivative of the flux function is a lower triangular matrix. There are no assumptions on genuine nonlinearity and strict hyperbolicity. Existence and uniqueness are proved except in a set with measure zero in the phase space and a set with measure zero in the flux function space where there is a one-parameter family of solutions. Travelling waves are used as an entropy condition and examples show that the Lax or Liu entropy conditions are not sufficient. An example shows that the solution does not necessarily depend continuously on the data. The model may be used to describe three-phase and tracer flow and flow in a neighborhood of a heterogeneity in porous media.
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