We consider an integro-differential conservation law that models the slow erosion of the granular flow. In the model, the flux contains an integral term in the space variable. Depending on the assumptions on the erosion rate, the solutions exhibit various types of singularities, including blowing up of the gradient. We establish existence of BV solutions and their continuous dependence on the data, obtaining a Lipschitz semigroup. For the case with continuous profile, the solutions are unique.

Amadori, D., Colombo, R., Guerra, G., Shen, W. (2014). Slow Erosion of Granular Flow: Continuous and Discontinuous Profiles. In Hyperbolic Problems: Theory, Numerics, Applications (pp.641-649). American Institute of Mathematical Sciences.

Slow Erosion of Granular Flow: Continuous and Discontinuous Profiles

GUERRA, GRAZIANO;
2014

Abstract

We consider an integro-differential conservation law that models the slow erosion of the granular flow. In the model, the flux contains an integral term in the space variable. Depending on the assumptions on the erosion rate, the solutions exhibit various types of singularities, including blowing up of the gradient. We establish existence of BV solutions and their continuous dependence on the data, obtaining a Lipschitz semigroup. For the case with continuous profile, the solutions are unique.
Slow Erosion; Granular Flow; Integro-differential Equation; Lipschitz Semigroup; Wave Front Tracking; Conservation Laws
English
14th International Conference on Hyperbolic Problems: Theory, Numerics and Applications
2012
Ancona, F; Bressan, A; Marcati, P; Marson, A.
Hyperbolic Problems: Theory, Numerics, Applications
978-1-60133-017-8
2014
8
641
649
http://www.aimsciences.org/books/am/AMVol8.html
none
Amadori, D., Colombo, R., Guerra, G., Shen, W. (2014). Slow Erosion of Granular Flow: Continuous and Discontinuous Profiles. In Hyperbolic Problems: Theory, Numerics, Applications (pp.641-649). American Institute of Mathematical Sciences.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/55463
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