A convection-diffusion problem in a network

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4 Scopus citations

Abstract

In recent years, it has become increasingly clear that the standard method of modeling hydrodynamic dispersion in groundwater flow by diffusion is often unsatisfactory. In the last few years, several authors have tried to overcome this problem by modeling subsurface flow by flow in a network. This has had some success and even some agreement with experiment. This work will lay the mathematical foundations for such models which, up to this point in time, have been studied only numerically. A well-posedness result is obtained for a class of these models. Some qualitative properties of solutions, such as positivity, ordering, and boundedness are also given.

Original languageEnglish (US)
Pages (from-to)223-240
Number of pages18
JournalApplied Mathematics and Computation
Volume112
Issue number2-3
DOIs
StatePublished - Jun 15 2000
Externally publishedYes

Keywords

  • Convection
  • Diffusion
  • Flow in porous media
  • Networks

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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