Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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: 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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DOI: https://doi.org/10.1090/qam/1306050
Article copyright: © Copyright 1994 American Mathematical Society

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