A Deposition Model: Riemann Problem and Flux-Function Limits of Solutions

Abstract EN

The Riemann solutions of a deposition model are shown.

A singular flux-function limit of the obtained Riemann solutions is considered.

As a result, it is shown that the Riemann solutions of the deposition model just converge to the Riemann solutions of the limit system, the scalar conservation law with a linear flux function involving discontinuous coefficient.

Especially, for some initial data, the two-shock Riemann solution of the deposition model tends to the delta-shock Riemann solution of the limit system; by contrast, for some initial data, the two-rarefaction-wave Riemann solution of the deposition model tends to the vacuum Riemann solution of the limit system.

Some numerical results exhibiting the formation processes of delta-shocks and vacuum states are presented.