Concentration in flux-function limits of solutions to a deposition model

TL;DR

This paper investigates the flux-function limit of solutions to a deposition model, showing convergence to delta-shock solutions and analyzing the concentration phenomena with numerical simulations.

Contribution

It provides a detailed analysis of concentration and delta-shock formation in the flux-function limit of a deposition model, including numerical simulations.

Findings

Riemann solutions converge to delta-shock solutions in the limit

Concentration phenomena are characterized and analyzed

Numerical simulations illustrate the concentration process

Abstract

This paper is concerned with a singular flux-function limit of the Riemann solutions to a deposition model. As a result, it is shown that the Riemann solutions to the deposition model just converge to the corresponding Riemann solutions to the limit system, which is one of typical models admitting delta-shocks. Especially, the phenomenon of concentration and the formation of delta-shocks in the limit are analyzed in detail, and the process of concentration is numerically simulated.