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

Xiaoming Wang

doi:10.3934/dcdsb.2010.13.489

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2010, Volume 13, Issue 2: 489-501. Doi: 10.3934/dcdsb.2010.13.489

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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: September 2010

Abstract / Introduction Related Papers Cited by

Abstract

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:

karst aquifer,
original and modified coupled continuum pipe-flow model (CCPF),
Hua's modified CCPF model,
conduit flow process (CFP),
existence of solution.

Mathematics Subject Classification: Primary: 86A05, 35Q35; Secondary: 76D03, 86A99, 76S05.

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