American Institute of Mathematical Sciences

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March  2010, 13(2): 489-501. doi: 10.3934/dcdsb.2010.13.489

On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer

Xiaoming Wang 1,

1. 

Department of Mathematics, Florida State University, Tallahassee, FL32306

Received  September 2009 Revised  October 2009 Published  December 2009

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.
Keywords: existence of solution., conduit flow process (CFP), Hua's modified CCPF model, karst aquifer, original and modified coupled continuum pipe-flow model (CCPF).
Mathematics Subject Classification: Primary: 86A05, 35Q35; Secondary: 76D03, 86A99, 76S0.
Citation: Xiaoming Wang. On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 489-501. doi: 10.3934/dcdsb.2010.13.489
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