Generalized Forchheimer flows in heterogeneous porous media

Emine Celik, Luan Hoang

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We study the generalized Forchheimer flows of slightly compressible fluids in heterogeneous porous media. The media's porosity and coefficients of the Forchheimer equation are functions of the spatial variables. The partial differential equation for the pressure is degenerate in its gradient and can be both singular and degenerate in the spatial variables. Suitable weighted Lebesgue norms for the pressure, its gradient and time derivative are estimated. The continuous dependence on the initial and boundary data is established for the pressure and its gradient with respect to those corresponding norms. Asymptotic estimates are derived even for unbounded boundary data as time tends to infinity.

Original languageEnglish
Article number1124
Pages (from-to)1124-1155
Number of pages32
JournalNonlinearity
Volume29
Issue number3
DOIs
StatePublished - Feb 16 2016

Keywords

  • Forchheimer
  • heterogeneous porous media
  • singular/degenerate PDE

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