On the spectrum of a rank two modification of a diagonal matrix for linearized fluxes modelling polydisperse sedimentation

The spectrum of a rank two modification of a diagonal matrix is calculated. The underlying matrix structure appears as the Jacobian matrix of a flux function of a first-order partial differential equation modelling dispersed solid-liquid flow. It is shown that, under physically reasonable conditions, there is a complete set of real roots of the characteristic polynomial. This contribution reexamines the analysis of (Basson, Berres and Burger, Appl. Math. Mod., 2008) by using the tools developed in (Donat and Mu let, Num. Meth. of PDE, 2009). The considered system belongs to a generic class of strictly hyperbolic, but non-genuinely nonlinear systems of conservation laws. For illustration, the solution of a benchmark initial-value problem is studied.