In this paper we study an integro-differential equation describing granular flow dynamics with slow erosion. This nonlinear partial differential equation is a conservation law where the flux contains an integral term. Through a generalized wave front tracking algorithm, approximate solutions are constructed and shown to converge strongly to a Lipschitz semigroup.
Colombo, R., Guerra, G., Shen, W. (2012). Lipschitz semigroup for an integro–differential equation for slow erosion. QUARTERLY OF APPLIED MATHEMATICS, 70(3), 539-578 [10.1090/S0033-569X-2012-01309-2].
Lipschitz semigroup for an integro–differential equation for slow erosion
GUERRA, GRAZIANO;
2012
Abstract
In this paper we study an integro-differential equation describing granular flow dynamics with slow erosion. This nonlinear partial differential equation is a conservation law where the flux contains an integral term. Through a generalized wave front tracking algorithm, approximate solutions are constructed and shown to converge strongly to a Lipschitz semigroup.
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