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Well-posedness Of A Non-local Model For Material Flow On Conveyor Belts

E. Rossi, J. Weißen, P. Goatin, S. Göttlich
Published 2019 · Mathematics

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In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensional splitting, we prove the convergence of the approximate solutions, where the main difficulty arises in the treatment of the discontinuity occurring in the flux function. In particular, we compare a Roe-type scheme to the well-established Lax-Friedrichs method and provide a numerical study highlighting the benefits of the Roe discretisation. Besides, we also prove the L1-Lipschitz continuous dependence on the initial datum, ensuring the uniqueness of the solution.
This paper references
10.1070/SM1970V010N02ABEH002156
FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
S. Kružkov (1970)
Kružhkov. First order quasilinear equations with several independent variables
S N. (1970)
Kružhkov (1970)
10.1090/S0025-5718-1980-0551288-3
Monotone difference approximations for scalar conservation laws
M. Crandall (1979)
10.1007/BF01396704
The method of fractional steps for conservation laws
M. Crandall (1980)
10.1090/S0025-5718-1983-0679435-6
On convergence of monotone finite difference schemes with variable spatial differencing
R. Sanders (1983)
10.2307/2938728
Numerical methods for conservation laws
R. LeVeque (1990)
10.1007/978-3-0348-8629-1_3
Scalar Conservation Laws
R. LeVeque (1992)
10.3934/DCDS.2003.9.1081
On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients
K. Karlsen (2003)
Improved stability estimates on general scalar balance laws
Magali L'ecureux-Mercier (2010)
10.1142/S0218202511500230
A CLASS OF NONLOCAL MODELS FOR PEDESTRIAN TRAFFIC
R. Colombo (2011)
10.1142/S021989161100255X
IMPROVED STABILITY ESTIMATES FOR GENERAL SCALAR CONSERVATION LAWS
Magali Lécureux-Mercier (2011)
10.4310/CMS.2015.V13.N2.A6
Hyperbolic predators vs parabolic preys
R. Colombo (2014)
10.1016/J.APM.2013.11.039
Modeling, simulation and validation of material flow on conveyor belts
S. Göttlich (2014)
10.1051/m2an/2014023
On the Numerical Integration of Scalar Nonlocal Conservation Laws
Paulo Amorim (2015)
10.1137/140975255
Nonlocal Systems of Conservation Laws in Several Space Dimensions
A. Aggarwal (2015)
10.1007/s00211-015-0717-6
Well-posedness of a conservation law with non-local flux arising in traffic flow modeling
Sebastien Blandin (2016)
10.1016/J.JDE.2017.05.015
Existence, uniqueness and regularity results on nonlocal balance laws
Alexander Keimer (2017)
10.1016/J.JMAA.2018.05.013
Existence, uniqueness and regularity of multi-dimensional nonlocal balance laws with damping
Alexander Keimer (2018)
10.1016/J.NONRWA.2018.07.027
Stability estimates for non-local scalar conservation laws
F. A. Chiarello (2018)



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