1,777 research outputs found
Toward a mathematical analysis for a model of suspension flowing down an inclined plane
We consider the Riemann problem of the dilute approximation equations with
spatiotemporally dependent volume fractions from the full model of suspension,
in which the particles settle to the solid substrate and the clear liquid film
flows over the sediment [Murisic et al., J. Fluid. Mech. {\bf{717}}, 203--231
(2013)]. We present a method to find shock waves, rarefaction waves for the
Riemann problem of this system. Our method is mainly based on [Smoller,
Springer-Verlag, New York, second edition, (1994)].Comment: Submitted to proceedings for EquaDiff201
A note on the spectral mapping theorem of quantum walk models
We discuss the description of eigenspace of a quantum walk model with an
associating linear operator in abstract settings of quantum walk including
the Szegedy walk on graphs. In particular, we provide the spectral mapping
theorem of without the spectral decomposition of . Arguments in this
direction reveal the eigenspaces of characterized by the generalized
kernels of linear operators given by .Comment: 17 page
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