Abstract:We address the Riemann and Cauchy problems for systems of n conservation laws in m unknowns which are subject to m − n constraints (m ≥ n). Such constrained systems generalize systems of conservation laws in standard form to include various examples of conservation laws in Physics and Engineering beyond gas dynamics, e.g., multi-phase flow in porous media. We prove local well-posedness of the Riemann problem and global existence of the Cauchy problem for initial data with sufficiently small total variation, in… Show more
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