On the Coupled Continuum Pipe Flow Model (CCPF) for Flows in Karst Aquifer
We show that the coupled continuum pipe flow model (CCPF) for flows in karst aquifers is ill-posed in the sense that no reasonable solution exists. We also demonstrate that Hua's modified CCPF model is ill-posed in 3D although it is well-posed in two spatial dimensions. a new modification of the original CCPF model that is consistent with basic physics is proposed and its well-posedness is proved here. We believe that this is the first physically relevant well-posed CCPF type model in 3D.
X. Wang, "On the Coupled Continuum Pipe Flow Model (CCPF) for Flows in Karst Aquifer," Discrete and Continuous Dynamical Systems - Series B, vol. 13, no. 2, pp. 489 - 501, American Institute of Mathematical Sciences (AIMS), Mar 2010.
The definitive version is available at https://doi.org/10.3934/dcdsb.2010.13.489
Mathematics and Statistics
Keywords and Phrases
Conduit Flow Process (CFP); Existence of Solution; Hua's Modified CCPF Model; Karst Aquifer; Original and Modified Coupled Continuum Pipe-Flow Model (CCPF)
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2010