Generalized Darcy-Oseen resolvent problem

Dagmar Medková, Mariya Ptashnyk*, Werner Varnhorn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 problems: 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 Methods in the Applied Sciences
Issue number6
Publication statusPublished - Apr 2016


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

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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