Journal
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
Volume 9, Issue 1, Pages 105-131Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219891612500038
Keywords
Granular flow; conservation law; integro-differential equation
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Funding
- NSF [DMS-0908047]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0908047] Funding Source: National Science Foundation
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We study a scalar integro-differential conservation law which was recently derived by the authors as the slow erosion limit of a granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one cannot adapt the standard theory of conservation laws. We construct approximate solutions with a fractional step method, by recomputing the integral term at each time step. A priori L-infinity bound and total variation estimates yield the convergence and global existence of solutions with bounded variation. Furthermore, we present a well-posedness analysis which establishes that these solutions are stable in the L-1 norm with respect to the initial data.
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