Analysis of miscible displacement through porous media with vanishing molecular diffusion and singular wells

Jérôme Droniou, Kyle S. Talbot

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

This article proves the existence of solutions to a model of incompressible miscible displacement through a porous medium, with zero molecular diffusion and modelling wells by spatial measures. We obtain the solution by passing to the limit on problems indexed by vanishing molecular diffusion coefficients. The proof employs cutoff functions to excise the supports of the measures and the discontinuities in the permeability tensor, thus enabling compensated compactness arguments used by Y. Amirat and A. Ziani for the analysis of the problem with L2 wells (Amirat and Ziani, 2004 ). We give a novel treatment of the diffusion-dispersion term, which requires delicate use of the Aubin-Simon lemma to ensure the strong convergence of the pressure gradient, owing to the troublesome lower-order terms introduced by the localisation procedure.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume35
Issue number1
DOIs
Publication statusPublished - Jan 2018

Keywords

  • Degenerate equations
  • Elliptic-parabolic system
  • Existence
  • Flow in porous medium
  • Measure data
  • Vanishing diffusion

Cite this

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Analysis of miscible displacement through porous media with vanishing molecular diffusion and singular wells. / Droniou, Jérôme; Talbot, Kyle S.

In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 35, No. 1, 01.2018, p. 1-25.

Research output: Contribution to journalArticleResearchpeer-review

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