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January/February 2010 A non-monotone nonlocal conservation law for dune morphodynamics
Nathaël Alibaud, Pascal Azerad, Damien Isèbe
Differential Integral Equations 23(1/2): 155-188 (January/February 2010). DOI: 10.57262/die/1356019392


We investigate a non-local, non-linear conservation law, first introduced by A.C. Fowler to describe morphodynamics of dunes, see [6, 7]. A remarkable feature is the violation of the maximum principle, which allows for erosion phenomenon. We prove well posedness for initial data in $L^2$ and give an explicit counterexample for the maximum principle. We also provide numerical simulations corroborating our theoretical results.


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Nathaël Alibaud. Pascal Azerad. Damien Isèbe. "A non-monotone nonlocal conservation law for dune morphodynamics." Differential Integral Equations 23 (1/2) 155 - 188, January/February 2010.


Published: January/February 2010
First available in Project Euclid: 20 December 2012

zbMATH: 1240.86010
MathSciNet: MR2588807
Digital Object Identifier: 10.57262/die/1356019392

Primary: 35B50 , 35L65 , 45K05 , 47G20 , 47J35 , 65M06

Rights: Copyright © 2010 Khayyam Publishing, Inc.

Vol.23 • No. 1/2 • January/February 2010
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