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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 10
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Articles

Viscous fluid-thin cylindrical elastic layer interaction: asymptotic analysis

G.P. PanasenkoInstitute Camille Jordan UMR CNRS 5208 University of Lyon, University of Saint-Etienne, 23, rue Dr Paul Michelon, 42023Saint-Etienne, France.Correspondence[email protected]
&
R. StavreSimion Stoilow Institute of Mathematics of the Romanian Academy, Research unit 6, P.O. Box 1-764, 014700Bucharest, Romania.
Pages 2032-2056 | Received 07 Jun 2013, Accepted 01 Apr 2014, Published online: 09 May 2014

References

  • Panasenko GP, Stavre R. Asymptotic analysis of the Stokes flow in a thin cylindrical elastic tube. Appl. Anal. 2012;91:1999–2027.
  • Efendiev Y, Pankov A. Numerical homogenization and correctors for nonlinear elliptic equations. SIAM J. Appl. Math. 2004;65:43–68.
  • Bakhvalov N, Panasenko G. Homogenisation: averaging processes in periodic media. Moscow: Nauka; 1984. Engl. Translation: Dordrecht: Kluwer; 1989.
  • Panasenko GP. Multi-scale modelling for structures and composites. Dordrecht: Springer; 2005.
  • Panasenko GP, Stavre R. Asymptotic analysis of a viscous fluid-thin plate interaction: periodic flow. Math. Models Meth. Appl. Sci. 2014. doi:10.1142/S0218202514500079.
  • Panasenko GP, Stavre R. Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall. J. Math. Pures Appl. 2006;85:558–579.
  • Mikelić A, Guidoboni G, Čanić S. Fluid-structure interaction in a pre-stressed tube with thick elastic walls. I. The stationary Stokes problem. Netw. Heterog. Media. 2007;2:397–423.
  • Temam R. Navier–Stokes equations. Amsterdam: North-Holland; 1977.

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