TY - JOUR
T1 - Existence and stability of traveling waves for an integro-differential equation for slow erosion
AU - Guerra, Graziano
AU - Shen, Wen
PY - 2014/1/1
Y1 - 2014/1/1
N2 - We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order nonlinear conservation law where the flux function includes an integral term. We show that there exist unique traveling wave solutions that connect profiles with equilibrium slope at ±∞. Such traveling waves take very different forms from those in standard conservation laws. Furthermore, we prove that the traveling wave profiles are locally stable, i.e., solutions with monotone initial data approach the traveling waves asymptotically as t→ + ∞.
AB - We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order nonlinear conservation law where the flux function includes an integral term. We show that there exist unique traveling wave solutions that connect profiles with equilibrium slope at ±∞. Such traveling waves take very different forms from those in standard conservation laws. Furthermore, we prove that the traveling wave profiles are locally stable, i.e., solutions with monotone initial data approach the traveling waves asymptotically as t→ + ∞.
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U2 - 10.1016/j.jde.2013.09.003
DO - 10.1016/j.jde.2013.09.003
M3 - Article
AN - SCOPUS:84885379762
SN - 0022-0396
VL - 256
SP - 253
EP - 282
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -