On a nonlocal dispersive equation modeling particle suspensions

Author:
Kevin Zumbrun

Journal:
Quart. Appl. Math. **57** (1999), 573-600

MSC:
Primary 35L65; Secondary 45K05, 76T99

DOI:
https://doi.org/10.1090/qam/1704419

MathSciNet review:
MR1704419

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Abstract | References | Similar Articles | Additional Information

Abstract: We study a nonlocal, scalar conservation law , modeling sedimentation of particles in a dilute fluid suspension, where is a symmetric smoothing kernel, and represents convolution. We show this to be a dispersive regularization of the Hopf equation, , analogous to KdV and certain dispersive difference schemes. Using the smoothing property of convolution and the physical principle of conservation of mass, we establish the global existence of smooth solutions.

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DOI:
https://doi.org/10.1090/qam/1704419

Article copyright:
© Copyright 1999
American Mathematical Society