Generalized Darcy–Oseen resolvent problem

Dagmar Medková, Mariya Ptashnyk (Lead / Corresponding author), Werner Varnhorn

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In this paper we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system we consider two auxiliary problem: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.
Original languageEnglish
Pages (from-to)1621-1630
Number of pages10
JournalMathematical Models and Methods in Applied Sciences
Issue number6
Early online date29 Feb 2016
Publication statusPublished - 29 Mar 2016


  • Darcy-Oseen resolven problem
  • semipermeable membrane
  • Brinkman-Darcy equations
  • fluid flow between free fluid domains and porous media
  • compact perturbations


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