Fluid flow in a layered medium

Authors:
G. W. Clark and R. E. Showalter

Journal:
Quart. Appl. Math. **52** (1994), 777-795

MSC:
Primary 76S05; Secondary 35Q35, 73B27

DOI:
https://doi.org/10.1090/qam/1306050

MathSciNet review:
MR1306050

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Abstract | References | Similar Articles | Additional Information

Abstract: A layered medium is modeled as a continuous distribution of relatively flat cells within a spatial region. Local flow within each cell as well as the exchange with the global flow over the region is modeled by a quasilinear parabolic system of partial differential equations, and the local geometry of the individual cells is included in the model. We introduce new terms to account for the secondary flux corresponding to either transverse flow across the cells or direct cell-to-cell diffusion driven by the global density gradient. The resulting initial-boundary-value problem is shown to be well-posed and to depend continuously on the parameter defining the type of interface condition on cell boundaries.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1306050

Article copyright:
© Copyright 1994
American Mathematical Society