In this paper we review some recent results for a model for granular flow that was proposed by Hadeler & Kuttler in [20]. In one space dimension, this model can be written as a 2 × 2 hyperbolic system of balance laws, in which the unknowns represent the thickness of the moving layer and the one of the resting layer. If the slope does not change its sign, the resulting system can be analyzed by means of the known theory, as for instance in the context of small C1 data or small BV data. Moreover, due to the special hyperbolicity properties of the system and of the special form of the source term, it is possible to enlarge the class of initial data for which global in time solutions exist. See [2, 29]. Further, we study the “slow erosion/deposition limit”, [3], where the thickness of the moving layer vanishes but the total mass of flowing down material remains positive. The limiting behavior for the slope of the mountain profile provides an entropy solution to a scalar integro-differential conservation law. A well-posedness analysis of this integro-differential equation is presented. Therefore, the solution found in the limit turns out to be unique.
A Hyperbolic Model for Granular Flow
AMADORI, DEBORA;
2010-01-01
Abstract
In this paper we review some recent results for a model for granular flow that was proposed by Hadeler & Kuttler in [20]. In one space dimension, this model can be written as a 2 × 2 hyperbolic system of balance laws, in which the unknowns represent the thickness of the moving layer and the one of the resting layer. If the slope does not change its sign, the resulting system can be analyzed by means of the known theory, as for instance in the context of small C1 data or small BV data. Moreover, due to the special hyperbolicity properties of the system and of the special form of the source term, it is possible to enlarge the class of initial data for which global in time solutions exist. See [2, 29]. Further, we study the “slow erosion/deposition limit”, [3], where the thickness of the moving layer vanishes but the total mass of flowing down material remains positive. The limiting behavior for the slope of the mountain profile provides an entropy solution to a scalar integro-differential conservation law. A well-posedness analysis of this integro-differential equation is presented. Therefore, the solution found in the limit turns out to be unique.Pubblicazioni consigliate
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