TY - JOUR
T1 - An integro-differential conservation law arising in a model of granular flow
AU - Amadori, Debora
AU - Shen, Wen
PY - 2012/3
Y1 - 2012/3
N2 - 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 ∞ 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.
AB - 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 ∞ 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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U2 - 10.1142/S0219891612500038
DO - 10.1142/S0219891612500038
M3 - Article
AN - SCOPUS:84859523742
VL - 9
SP - 105
EP - 131
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
SN - 0219-8916
IS - 1
ER -