This contribution is a condensed version of an extended paper, where a contact manifold emerging in the interior of the phase space of a specific hyperbolic system of two nonlinear conservation laws is examined. The governing equations are modelling bidisperse suspensions, which consist of two types of small particles differing in size and viscosity that are dispersed in a viscous fluid. Based on the calculation of characteristic speeds, the elementary waves with the origin as left Riemann datum and a general right state in the phase space are classified. In particular, the dependence of the solution structure of this Riemann problem on the contact manifold is elaborated.
system of nonlinear conservation laws bidisperse suspension characteristic velocities contact manifold Hugoniot locus Riemann problem
D.K. Basson, S. Berres and R. Bürger. On models of polydisperse sedimentation with particle-size-specific hindered-settling factors. Appl. Math. Modelling, 33 (2009), 1815–1835.MathSciNetCrossRefMATHGoogle Scholar
S. Berres and P. Castañeda. Contact manifolds in a hyperbolic system of two nonlinear conservation laws, http://arxiv.org/abs/1501.06019, (2015).Google Scholar
S. Berres and T. Voitovich. On the spectrum of a rank two modification of a diagonal matrix for linearized fluxes modelling polydisperse sedimentation. Proc. Symposia in Appl. Math., 67(2) (2009), 409–418.MathSciNetCrossRefMATHGoogle Scholar
A. de Souza. Stability of singular fundamental solutions under perturbations for flow in porous media. Mat. Aplic. Comp., 11 (1992), 73–115.MathSciNetMATHGoogle Scholar
F. Furtado. Structural Stability of Nonlinear Waves for Conservation Laws. PhD Thesis, NYU (1989).Google Scholar
P. Rodríguez-Bermúdez and D. Marchesin. Riemann solutions for vertical flow of three phases in porous media: simple cases. J. Hyperbolic Differ. Equ., 10(2) (2013), 335–370.MathSciNetCrossRefMATHGoogle Scholar